According to my experience (and again, that's the only thing I know), that's not even remotely true.
When I interviewed a couple years ago, I made sure to interview at FAANG (specifically Facebook, Google, Netflix) and I also interviewed at half dozen big public companies in the same couple months (among which Oracle, Salesforce, Cisco, Juniper, Palo Alto Networks). I didn't interview at any private company (Uber, AirBnB, ...), since I was coming out of the startup world and I wanted liquid compensation.
The FAANG offers that came back were all significantly higher than the other ones, and the constant was certainly me (a software engineer with 7 years of experience at the time and a BS + MS in Computer Engineering).
All the FAANG offers (luckily I got an offer from all the 3 I interviewed at) were at a total liquid compensation of $~400-450k/y (annualized cash + RSU), and I'm certainly not in the top 10% of their tech workforce, not even remotely close, I come in as a generalist with some ops experience who spent a couple months studying algorithms and data structures. I don't even have an active GitHub profile.
All the other non-FAANG tech companies (I got an offer from 4) were at a total liquid compensation of $~220k/y (annualized cash + RSU).
The only other companies who matched the FAANG offers were a couple of hedge funds on the East Coast, but I didn't want to relocate and I wanted to keep working for a tech company.
In the end, I joined Google.
So, I'm just reporting my own personal experience based on the data I directly experienced (I have PDFs of all the offers :-)). Feel free to ask any follow up question, I love educating software engineers on their real market value, since I think many sell themselves too short in this thriving market.