In all the years i've shot caribou in Alaska, and i've shot quite a few, i've never had one "tainted" from the rut or anything else.
The only meat i've had go bad was when one time i was stranded in the Brooks Range for quite a while, and lost some sheep meat before i got it all smoked!
Now bear meat, that's a diff story, as it really depends on what they've been eating as to wether you will want to eat them!!
Drilling Man