In the US, you are correct. By default, it is illegal for a company to negotiate terms with any individual covered by a union, even if that individual is not a dues paying member of the union.
Technically, you are allowed negotiate, but it is illegal for the company to accept and it is not legally binding, so it is functionally equivalent to it being illegal to negotiate terms for yourself (assuming you want to negotiate, it is obviously better at preventing unilateral corporate abuse as the corporation would be on the hook for tricking you).
I believe you can negotiate if the union lets you, but by default you can not. Also, you can not unilaterally waive union representation either, even if you are not a member, so if the union does not allow it you would need to convince 50% of the covered individuals to change the rules or dissolve the union.