Did Corporate authorize it?
I believe it was in-fact a Corporate decision to do this in collaboration with each and every Dunder mufflin Branches not just Scarton. Cause the AD crew tell Micheal and others how did they do it in the other branches, and wanted to do the same here as well but micheal develops creative difference and finally tries to show the AD crew a much better version with a on the spot composed song and all which still gets rejected.
Or was this one of Michael's blunders and Corporate had no choice but
to just let it slide and try to utilize it as free PR
No Definetly Not, if it had been one of Micheal's plot he would have been better prepared to Make it more colorful and inject himself in any primary roles, instead of just the song the crew had created. But instead ended up waving like in the final product.
Also Micheal lacked the vision to look at the entire company progressing, he was someone who was excellent as a Branch manager and was really never bothered about Dunder mifflin as a whole company instead of just relating it to a single branch, He was extremely good as a branch manager as when the company was getting sold to sabre scranton was the only branch which survives.
In-universe, who authorized and signed the contract for the document
crew to come film
so I do strongly believe this decision came from above Miceal, maybe Jan, David or any other higher ups.