Good point. Here’s how I handled it:
I introduced myself as a “supporter of company X” when making these pitches. That way, I don’t come off as weird by saying “I’m applying for a role at company X” and I’m also not misrepresenting myself as an employee.
And yes, you do have to be careful about not pitching companies that have already been pitched and/or will be pitched in the immediate future. When I was pitching, I made sure to either 1) choose companies where I at least kind of knew the person I was pitching to (so it wouldn’t look as bad if they had already been pitched), and/or 2) pitch to companies that weren’t that public with their information and little more obscure (so I could reasonably assume that they hadn’t been pitched, and probably wouldn’t be in the near future).
I guess it’s possible that it could backfire, but you can de-risk it a lot.