It depends on the specific claim. If it's a blanket statement like "

big tech can't track you

" then yes, that would be false. What VPNs are good for is encrypting content so your ISP or any man-in-the-middle can't see the content of your web traffic. You're correct, that hiding your IP address has limited utility in hiding your identity from the sites you visit. There is enough unique information being sent to form that browser fingerprint. Products like Avast AntiTrack are specifically meant to scramble that fingerprint data and prevent your identification and tracking.