They want you to be intimidated by their reputation because it's easier if you make concessions first hoping to get some benefit later. Keep in mind, these are business people and they're very good at it (otherwise they wouldn't be giants). The benefit will never materialize. Working for free just means it was an easy win and you left money on the table.

Do not work for free. Large companies have a shit ton of money. All you need to do is provide an economical argument in the form of your rate (which should take into account their expenses for having an employee / team work on it instead, hint: 2 x total compensation). Getting paid is just a matter of the guy who reached out to you to talk to his skip manager to get a verbal 'ok', and then the accounting department takes care of it. They're not going to pass on you just because you asked to be paid for your time - a business is used to paying for services. If they do pass on you without even negotiating your rate, then they were definitely not serious and nothing good would have come out of it for you.

Source: dev working at FAANG with 3rd party companies.