When I was at Facebook, 2013–2016, the rumor I heard was the opposite.

It was my understanding that Google practically had a policy of counter-offering anyone who got an offer from Facebook, and that seeking an offer from Facebook was a strategy Googlers used to up their compensation.

Ironically, Facebook had the opposite policy: If you get an offer from elsewhere, it was Facebook’s policy not to counter-offer. Facebook’s view is that if they start counter-offering, they will get into a compensation arms race. And besides, if you really want to go work somewhere else, then maybe you should. There are lots of people who would love to work at Facebook; they don’t need to try to convince you to stay if you want to leave. And if you’re just bluffing, well good on them for not falling for it.