There seems to be an indefinable line separating tragedy from comedy, and at times it's hard to know when to stop. I'm one of those people who have to fight an irrepressible urge to laugh when I see someone slip and fall, and not because I think it's hilarious that someone might injure themselves - I just can't help it. I'm not alone in this, it's quite common, and is no doubt the reason that slapstick became so popular. Some Mothers do 'ave 'em was one of the most successful TV comedy series ever, and was based entirely on the slapstick principal.
The Amy Winehouse joke is funny in the same way - she's a tragic figure in several ways, and this leaves her wide open to this kind of joke. I very much doubt that she cares in the slightest as she reads her latest bank statement, and nor would I. It's one of the costs of fame.