What to do about a citation that may be wrong
A polite way to deal with this is to say &quot;We need the following known result (c.f. [A] and [B])  and include the proof for the convenience of the reader.&quot;  If someone writes you to clarify before this is finalized, you can revise.
If you are worried about giving credit that is inappropriate, take a moment and reflect on how citation counts are often misleading.  Your primary concern is the reader (including referees) and the above allows them to be as informed as they need to be.
If someone (say a referee) asks you to cite [B] for the proof, ask for a page or theorem reference.