Very fun

That's an interesting article, but many of the examples ("funner", "funnest", "so fun") seem non-standard English to me. It's OK to say "a fun time", or "a fun activity", because here it's a noun used as a qualifier - like "chicken soup" or "a biology class". But I wouldn't say "very fun".

On peut dire "Good fun" "Great fun" "lots of fun" ou "very funny" mais jamais "very fun" ça ne marche pas. :)

Agree with Ian, with the added detail that “very funny” in English does not have the same meaning as his other 3 examples, with “fun” being something enjoyable and causing a good time, and “funny” being something humourous that makes one laugh. There doesn’t seem to be the same distinction in French as “amusant”, ”drôle” and “rigolo” were all given as alternative acceptable answers for “fun” in this exercise. 

On the other hand, "really fun" is acceptable I think, even when "fun" is clearly being used as an adjective, such as "we had a really fun time".

I think there's a subtle difference in meaning between funny and fun (as a potential adjective).

You can say: "There's a funny smell," meaning it smells strange. But you couldn't say "there's a fun smell."

Just imagine what a lesson on the use of fun vs funny would be like for poor French speakers!

"Thanks! It was a very fun event/time/evening/party." Grammarians will frown upon this, but it has crept into somewhat normal usage. English is pretty flexible - if people use something enough it becomes "okay." I myself think this is something a child would say and that I would correct if that child was a relative or someone close. But if anyone else said that to me i wouldn't quibble and would simply reply. "Yeah, I had lots of fun too". I have learned that trying to impose English rules on the French language doesn't work and can be dangerous and frustrating. I have absolutely no problem with "très amusant/rigolo/drôle"