First, I LOVE your new avatar!!! Silly Cedric!
I've never heard of dogs being allergic to sun, but my step-sister is, so if it's possible with people, it's probably possible with dogs. And, to clarify, it's not that she burns fast in the sun (she tans nicely actually), she just gets a rash, which can even turn scabby
Here's a weird one, I have a friend who's skin is sensitive/allergic to water. Seriously, you'd think it'd be impossible, or it was just the soap or something, but it's not. When her skin gets wet (shower, swimming, rain, whatever), even with pure H2O, she gets hives. They go away within a couple hours, but she just always is kind of itchy and gross poor girl.