We were there a little over a month ago and the wheat hamburger buns were at the CS place in between POTC and Splash Mountain. Sorry, but in years and years of going to WDW, I have yet to figure out the name of the place! Half the time, I can't even get in, because doors are locked, but people appear to be eating meals they'd purchased inside outside.
We also had these buns at Casey's.
Anyway, we eat wheat or whole-grain buns and bread at home (I'm actually partial to flax and oatmeal bread), but the buns we had at WDW last month were soooooo dry and crumbly. The burger was really inedible. As soon as you put ketchup or anything "wet" on it, it pretty much disappeared into the burger. After two bites, I had no choice but to eat it with a fork and knife.
The bun for the hot dogs for both DH & I broke after taking our first bites. After a couple bites with the ketchup and mustard, it turned into more crumbly mush.
The buns were bad. But the burgers they put into the bun were horrid. I know WDW has had good burger years and bad burger years ... we're in the bad burger trend right now.
On a positive note, some of the CS is better now, IMO, with the whole-grain breads. We got a pannini at Pinocchio's Village Haus on whole-grain bread, and it really held up well and made the sandwich feel much more like a "meal." I've had this before pre-whole-grain bread, and it's much more filling on the newer whole-grain bread.
We go to WDW and look forward to enjoying some junk, too. I think we're taking hot dogs and CS burgers off the list for now.