It's got just enough truth to it that one can't straight-out call it a lie (because it's referring vaguely to the possibility, not saying it happens everywhere or in specific, falsifiable, cases), but it's basically propaganda.
In reality, by definition, most people (and in fact nearly everyone), including most people on here, are not getting pay above the rates that a union would be able to negotiate, even if you assume that a given union coming into your workplace would negotiate for something approximating flat rates or scheduled rates. The data all show that going from non-union to union increases compensation by significant amounts—I've seen numbers from ~11% to ~20%, so it probably varies across time.
I hope that one day you, too, can come under union representation, even if it's against your own desires, so that you can see how much more money you'll get, how much better you can be treated, and how much more your voice will matter.
If feel like there's a missing /s there. If only we did have a way of compensating someone for their labor. Maybe we could call it a salary? If you're counting on a bonus to compensate for a lack in salary, then you should be having your union do its job and negotiate higher base salary. There's a reason a bonus is not called salary.
FYI, this is in now way a show a support for unionizing on my behalf. Just pointing out the fallacy of the argument as presented