I'm guessing the words you mentioned are all close because they are modern. In the same way that many words that have entered Japanese in the last 200 years are actually English or Portuguese words brought in by foreigners and adapted to the local pronunciation. You can cheat so much in Japanese by simply learning to read katakana and finding all the English words.
Hungarian’s closest relatives are Khanty and Mansi. While Hungarian, Finnish and Estonian are indeed in the same Uralic language family, they were at the very opposite ends of the dialect continuum that ultimately produced that language family, and they no longer bear any close relationship.
> Exceptions: Italian uses pomodoro, and some other languages use a word similar to the Italian one. Mandarin Chinese is another exception!
"paradicsom" is not similar to pomodoro, in either pronounciation or meaning.
And if the author has made one so simple mistake, we have to assume there are many more with the more exotic languages.
Edited to add: According to Wikipedia [0], the original Hungarian expression was also "apple of paradise," which then got shortened to just paradiscom. It also points out that the Italian pomodoro is literally "apple of gold." I guess the far-flung origins were thought of as paradisical...
[0] https://hu.wikipedia.org/wiki/Paradicsom_(n%C3%B6v%C3%A9nyfa...
tea - tea (different pronunciation) pineapple - ananász orange - narancs taxi - taxi (slightly different pronunciation) tomato - paradicsom
now let's look at the article's champions coffee - kávé chocolate - csokoládé
both the same origin, but distorted so much, that i could not order those things in starbucks...
so in my books, taxi is the winner