An interesting theory, but there are good reasons to doubt the claim, including the fact that woolly sheep are a recent product of human breeding, and that wild sheep are not even native to the same areas blackberries grow.

There's tonnes of blackthorn and a lot of sheep in the UK and I've never heard it to be problematic. Sheep ate pretty dim, but bramble is definitely not thorny/spiney enough to get caught bar the odd occasion. I'm sure I heard about a shrub (African maybe) that sheep can get completely ensnared in and die, but can't find it!