Which amps cannot be repaired locally?

First any amp can be repaired by local tech if one isn't dumb and willing to work adn troubleshoot the unit.

Check if thechies are certain about this part and try to find it through digikey, mouser or newark. Also that part has likely a manufacturer's name and one can share parameters of this chip with you so you can find similar on major electronic parts dealers. If found IC of a different brand, it will have different part number, but same functions. You'll need to do the homework that local techies are unwilling to do. A controller board and Controller Board IC are two different entities. One you'd want to replace board as a whole thing(The American Way) and another you specifically diagnose in details which part has failed. You should verify that they've diagnosed IC in particular on the Controller Board and find one that matches parameters of the failed one. IC chips go in and out of production frequent just like computers so what was placed there 2 years ago may not be in production anymore.

And finally, there are certain legal procedures against smart S-holes similar to Niles. You can claim your money back for the unit they refuse to provide parts after a couple of years of usage. I betcha you didn't sign any papers that you're mandatory supposed to bring unit to only their own repair facility. They will probably get around much cheaper giving you refund than hiring a councelor at your local area.

There are other companies that function that way. The most "famous/infamous" is Levinson. Or worse; the U.S. importer of Sonus Faber won't even repair their speakers unless you can prove it was purchased from authorized U.S. retailer.

For a moment I was thinking to initiate the discussion call "Ripoff Schema Champions" and thinking of it now. Check on that later.

This is america guys, what few consumer laws there are ,are not enforced.

Schubert is correct. I found Spectral to be downright rude when I tried to service one of their preamps. It had a shorted transistor in it. I was basically told if I worked on it, they would be able to tell, and would never work on the unit again.