The statement about contractors not having a right to bargain as a union isn't quite the full story. What contractors don't have is a right to have a union as the sole bargaining unit for all contractors. With employees, the union bargains on behalf of all employees whether they're members of the union or not. Contractors have every right to form a union and have it bargain on their behalf, but it can only bargain on behalf of those contractors who're members. If you aren't a member, you negotiate your own terms. And the company can't refuse to negotiate with the union because they aren't negotiating with the union, they're negotiating with you with the union acting as your agent. They can of course refuse to negotiate with you, but they could do that anyway (and frankly any sane contractor has an attorney involved in contract negotiations to make sure there aren't any hidden loopholes or gotchas in the contract, so refusing to deal with a representative would be a red flag that these aren't negotiations) and the basic idea behind a union is that refusing to deal with the union cuts the company off from so many contractors that they can't afford to do that.
The thing to be wary of is joining a union or other organization where the management has the right to overrule the membership. That's when things always go badly.