They know it's you.
They just compare the set of friends with whom you spoke using your original number and with whom this new number speaks now. Otherwise you are right.
They use a probability factor to identify similarity with other users. If the similarities match high, they internally identify it as a probable identical profile.
But for this to happen successfully, they would have to use the first profile that didn’t agree to new terms and compare it to new profile that did agree to new terms.
Btw, somewhere in Facebook land they are trying to workaround this hack. Which means FTC should be all over this.
Connecting to several of your old friends is more than enough to identify someone with an incredibly high level of confidence.
(Example list of people: someone at your job or a friend, another friend, your mother.)
Obscure, please, in all seriousness - but fund the EFF, and vote for people who support data privacy vocally.