Here's the thing - having worked there briefly you are now on the top of their lists. You're part of the exclusive club in recruiters' eyes, whether it actually sets you apart or not. I worked at Amazon for a few months, and regularly get contacted by Amazon recruiters. But never Facebook, etc.

I did not notice much of a difference in recruiter intensity before or after my short stint there.

(But I was at eg Google before at some other point in my career.)