Social security office knows that there are records in that database without confirmed deaths.

They use multiple techniques and data sources to determine who to send benefits to.

This is not news to the SSA.

https://oig.ssa.gov/assets/uploads/a-06-21-51022.pdf

"AGENCY COMMENTS SSA disagreed with our recommendations. Agency officials stated that most of the records discussed in the report involve numberholders who do not currently receive SSA payment"

So, they can do better, but sure, they are sending some relatively small number of checks out to dead people. That doesn't mean Musk needs to lie about the the program as an excuse to cut the whole thing, which is actually what we see playing out.