They might be running afoul of discrimination laws if they only interview US citizens to cut down on their workload for fake interviews, but I'd guess someone this careful (e.g. not actually submitting the greencard sponsorship where many employers would with a wink and a nod) is likely careful enough to not filter candidates on such obvious things either.
It's a problem with the h1b (and green card) program itself, not OPs behavior. If anything, OP is probably in the top few percentile of ethical businesses/managers if they are actually denying the sponsorships because they made a good faith attempt to test to see if the local market had appropriate candidates.