The person correcting a small fact may be protecting a larger conclusion from drifting.

Small corrections get heard as pedantry, and sometimes that is what they are. Often, though, the person is looking further down the line, at the conclusion that will be built on the fact and retold with the error compounding each time. A slightly wrong number becomes a badly wrong decision three meetings later. Fixing it early is cheap and looks fussy; fixing it late is expensive and looks like wisdom.

Take the correction without treating it as an attack, and say thank you. When you are the one correcting, say why it matters rather than only that it is wrong.