The idea is that something being offensive is inherently subjective. If you claim being offended, you are offended. Offending people - at least people that Google management is inclined to listen to - is a no-no. Consequently, if you want to veto a speaker, you just need to proclaim your offense. There's no proof required because there's no proof possible - there's no objective test for being offended, only your feelings, of which you are the only judge. As soon as you decided to proclaim your veto, that's it, the deed is done.
Why people at Google decided to veto PETA speaker - who knows. But there's no point in digging deeper than that and trying to find logic in it - there's no logic in this setup.
> People will just start objecting to any talks.
That'd work if the decision were impartial. But an anonymous "employee working on Talks at Google" doesn't have to be impartial.