When you first asked the question, my feeling was that that can't be right. A family can't knowingly get two payments. But, since we cannot find where that is specifically stated and what is stated seems to say just the opposite, I would claim it.
I'll give you an example where I've specifically seen where two payments are allowed: divorced parents alternate years on who claims the kid, as a dependent. Mom got the $1400 stimulus payment because 2020 was her year. Dad can still claim the $1400 Recovery Rebate Credit, for the same child , on his 2021 return.
