I still ask why a county sheriff in Arizona would be interested in a forged document taken from the internet. If Arpaio had said something to the extent that by Arizona law requirements for eligibility for POTUSA to be on the ballot a proof of citizenship birth had to be given the dots to Obaba’s eligibility would have been connected. Nothing to do with Federal action just that Obama was not eligible for POTUSA. perhaps this is where/when Fed action could come into play.
If you look at the bigger picture, and I am sure he has, you have a point but, he was asked by 250 signers of a petition to look into the “fact” that what was shown to the public on 4/27 was not genuine. He was handed preliminary evidence that convinced him to look into it further. And as he stated his initial thought was to be able to clear this issue up. That didn’t happen.
He was trying to placate his political base without committing to actually doing anything in the legal arena. Hence a “posse” of non-LEO volunteers. Since it was not an official investigation by professional LEOs, I doubt he could take it to a grand jury if he wanted to.
So he has the best of both worlds - firing up potential voters while never having to prove anything in court.