What if the recruiter tells you that Google/FB/etc reviewed your resume and you didn't make the cut? (When in actuality they just don't want to pay the commission)
You wouldn't dislike them, but you might then not apply for a job there (thinking you had already been turned down once), and then Google/FB/etc misses out on any chance to hire you.
I can't imagine getting a bad impression of Google from what a random recruiter tells me.