1. Because it makes him seem like a martyr to the cause without him actually having to do anything, just like when he implied he couldn't give a speech on the embassy balcony because Clinton's forces were about to kill him with a sniper rifle. (http://www.angrypatriotmovement.com/wikileaks-huge-hillary-a...) ...so he had his followers tune into a 3AM webcast instead, which ended up just being a promo sales pitch for his book. He is excellent at marketing.
2. The truth will not "come out regardless" if he was lying. It's very hard to prove a negative. Even if the embassy puts out an announcement saying "As far as we know, his internet is fine," Wikileaks can just say "The embassy is in cahoots with the Americans," or "It was cut earlier, and sources told me it was the gubbment." No one will care much at that point, his martyrdom point will have been made.
Time will tell. You could be right, you could be not. I believe that if Assange says something that is not truthful that reflects bad on Ecuador (one possible explanation is that Ecuador blocked his access) that they would make a statement if what he said was incorrect. And I'd believe them over Assange if that's what it came to.
Note that Wikileaks is making the claim not Assange and they are not the same entity (they'd have to, given that Assange can't go online).
Now, it could all be not true but what would be the point of lying about this when the truth will come out regardless?