The common misunderstanding is that "holding out" isn't limited to aviation. It's just a phrase that refers to letting the public know of availability.
The problem in aviation isn't "holding out." It's holding out something that you're not entitled to do without operating certificates. IOW, there's nothing wrong with "holding out" your availability to act as a pilot in a Part 91 operation, to engage in any of the activities listed in 119.1(e), to flight instruct as a CFI, to ferry aircraft, etc.
as jcaplins said, it's not "holding out" that's the problem, it's holding out availability to act as a carrier that requires operating certificates you don't have.