I think we're conditioned to believing that "fat" means "obese." Generally speaking, I'm sure an obese fish is as unhealthy as say, an obese person ... but to that end I've never seen an obese fish. I'm no fish researcher but I'm not sure the condition even really exists.
Most of the fish in captivity are undernourished. I have yet to see a fish in a fish tank that could hold a candle to how wide his or her wild counterparts are. Tangs in the wild are wide, wide fish, like 2" or even 3" wide or more. The widest tangs I see in capitivity are rarely more than say 1.5" wide.
But, having said all that .. the "guys with beer guts" description sorta troubles me. If the guts are protuding, this is not good. That could be a blockage. I had a blenny that did have a protuding belly and apparently that's not uncommon for blennies but it's not common at all for tangs. So that might actually be a problem.
Can you post any pictures?