So the company in question has what legal right to investigate the employees of their contractors? Did the contractor’s employees sign off on this? It seems unlikely.

A better remedy would be to fire the contract partner if you feel the work isn’t meeting the value you expect.

You can investigate whatever you want.

If you read the article and look at the differences, they fired the Equifax employees outright. They "flagged" a bunch of contractors. That almost certainly means they sent that list of contractors to their employer companies and requested additional verification of hours and/or requested they be removed from their projects.

I’m more interested at what point they’re violating the FCRA, because I feel like they have to be somehow

That’s actually illegal on the part of the company.