Yeah, that’s one of those things where people think the first place they saw a thing is the same as its origin.
‘That’s what SHE said’ (or equivalent ways of highlighting an innuendo such as ‘said the actress to the bishop’) is a really old joke-form that probably dates back to Victorian music-hall comedy or before.
It’s not tremendously easy to find exact examples of ‘that’s what she said’ going back that far, but it is trivial to prove that it’s not a Michael Scott thing - here’s someone on the SDMB discussing it several years before The Office first aired in the USA.
(It’s probably something Ricky Gervaise also said in the original series of The Office, but he didn’t invent it either - it’s old)