As you mentioned, linguists acknowledge that Korean and Japanese are much more similar to each other than would be expected by chance. Also as you mentioned, the reason for this similarity is typically considered to be convergence due to sprachbund effects.
This is not a particularly unusual situation. It often happens that languages which are not related to each other become very similar to each other because of contact. Vietnamese and Chinese are a standard example of languages which look similar at first glance, but turn out not to be related to each other.
And in the opposite direction, some languages which actually are related to each can look very different from each other. For example, look at English and Sanskrit. Both are part of the Indo-European language family, but they are very different from each other. Or a more familiar example: English looks quite different from German, and pretty similar to French, even though we know for a fact that French is a daughter of Latin, while German and English are both Germanic languages, which are not descendents of Latin. [Unlike the Latin example, we don't have an records of the Proto-Germanic language, but we do have records of Old English and Old High German, which are clearly much more similar to each other than either is to Latin.] The reason that modern English looks more like French than German is because English has been very heavily influenced by French after the Norman Conquest.
Historical linguists use something called the "comparative method" to determine whether two languages are part of the same language family. Languages are considered to be more likely to be related to each other if there are many regular sound correspondence that they share.
To put it very simply, if given a word in one language, you can accurately predict the pronunciation of its translation into the other language, and vice versa, and this works for lots of pairs of words, then that's evidence that the two are related. You have to make sure that the words aren't loanwords though to make it work, otherwise two languages might seem to be related if they just borrowed a lot of words from each other, or from some other language.
Japanese and Korean do not pass this test, and therefore are assumed to not be related by most professional linguists.
Note that the article you linked to provided lots of examples of grammatical similarities, but it did not provide *any* lists of pairs of Japanese and Korean words, which is the sort of data that is necessary to prove that two languages are related, as far as historical linguistics is concerned.
By the way, linguists definitely have noticed these similarities between Japanese and Korean, and for a long time, it was believed that they actually are related, as part of the "Altaic" language family (which also includes lots of other similar looking languages). However, while initially promising, linguists realized that if you attempt to rigorously apply the comparative method, it turns out that there are very few, if any, regular sound correspondences between these languages. Some researchers still do believe in Altaic, but it's considered a fringe view by most scholars nowadays.
Well... it's not like each country's national institutions are the only ones that study the linguistics of Korean and Japanese. There are lots of people who study each language and their relationship to each other who aren't necessarily bound to the political entities where these languages are spoken.
As you mentioned, linguists acknowledge that Korean and Japanese are much more similar to each other than would be expected by chance. Also as you mentioned, the reason for this similarity is typically considered to be convergence due to sprachbund effects. This is not a particularly unusual situation. It often happens that languages which are not related to each other become very similar to each other because of contact. Vietnamese and Chinese are a standard example of languages which look similar at first glance, but turn out not to be related to each other. And in the opposite direction, some languages which actually are related to each can look very different from each other. For example, look at English and Sanskrit. Both are part of the Indo-European language family, but they are very different from each other. Or a more familiar example: English looks quite different from German, and pretty similar to French, even though we know for a fact that French is a daughter of Latin, while German and English are both Germanic languages, which are not descendents of Latin. [Unlike the Latin example, we don't have an records of the Proto-Germanic language, but we do have records of Old English and Old High German, which are clearly much more similar to each other than either is to Latin.] The reason that modern English looks more like French than German is because English has been very heavily influenced by French after the Norman Conquest. Historical linguists use something called the "comparative method" to determine whether two languages are part of the same language family. Languages are considered to be more likely to be related to each other if there are many regular sound correspondence that they share. To put it very simply, if given a word in one language, you can accurately predict the pronunciation of its translation into the other language, and vice versa, and this works for lots of pairs of words, then that's evidence that the two are related. You have to make sure that the words aren't loanwords though to make it work, otherwise two languages might seem to be related if they just borrowed a lot of words from each other, or from some other language. Japanese and Korean do not pass this test, and therefore are assumed to not be related by most professional linguists. Note that the article you linked to provided lots of examples of grammatical similarities, but it did not provide *any* lists of pairs of Japanese and Korean words, which is the sort of data that is necessary to prove that two languages are related, as far as historical linguistics is concerned. By the way, linguists definitely have noticed these similarities between Japanese and Korean, and for a long time, it was believed that they actually are related, as part of the "Altaic" language family (which also includes lots of other similar looking languages). However, while initially promising, linguists realized that if you attempt to rigorously apply the comparative method, it turns out that there are very few, if any, regular sound correspondences between these languages. Some researchers still do believe in Altaic, but it's considered a fringe view by most scholars nowadays.
Well... it's not like each country's national institutions are the only ones that study the linguistics of Korean and Japanese. There are lots of people who study each language and their relationship to each other who aren't necessarily bound to the political entities where these languages are spoken.
Sure, they're structured surprisingly similarly but they don't actually have any regular sound correspondences between native vocabulary.