There's mounting evidence that prions are not 'infective' at all. That they have a proper role in brain electrochemistry/electromagnetism.
Prions have copper atoms in them, which keeps them the right shape to do their job. In areas of copper poor soil, manganese substitutes for the copper atoms and distorts the prions. They then don't do their job properly, hence the symptoms of the diseases like BSE, CJD etc.
For example, in a flock of sheep that spend the summer on the mountains mixing together, only half get scrapie. This half return to one valley in the winter, the other half, that don't get scrapie, return to another valley. One valley has copper sufficient soil, the other copper deficient soil. If scrapie were infective, you'd expect some of both flocks to get it equally.

I've just been talking about this with my dad this weekend, re scrapie, a sheep disease associated with prions.
The main person working on this in the UK is Professor Brown, at Cambridge University. I think there is work going on at Toronto University too. I'll see if dad has some direct references ( he will have!)

So - the answer might be - that beef is safe to eat and the prions in it are not a problem!