It is purely a tax decision on how this person is hired. If they worked there as a w-2 employee, would the OP be similarly hand wringing?
Contract to Hire is a very normal way to hire. Subcontracting at least SOME of the work is actually a sign of specialization, and can create much better work then just doing everything in house.
The OP has no idea how the style he likes so much was actually created. It could have been created by a Slovakian national working on an internship for all he knows
If you want quality signoff agreements, then make those. Don't get all scared the first time you find one part of the project is not 100% done by staff that's been there for decades. It's a company. It hires people. That's what makes a company different than a freelancer.
And, yep, you may have overreacted. Companies subcontract work. That's what they do. Among other things, this is how firms train and audition new people -- by hiring them as subcontractors.
If you pay Company X for the work, you get work with Company X's name on it. If something goes wrong, you get to blame the whole company -- they don't get to dodge the blame by passing it on to their subcontractor. But, in return, you shouldn't expect the right to micromanage the internal affairs of the company.
Of course, it's also possible that you dodged a bullet. Who knows? If the contractor couldn't convince you to stay on as a client, using arguments like the ones above, that might be a sign that you weren't likely to get along well together. Client-contractor relationships are a tricky business. Often you are required to make gut-level decisions.