They suck at propaganda because the claims are unverifiable lies? That's not really the point of propaganda. Did it scare a number of employees into voting no on a union? If yes, then they propaganda'd just fine.
I'm not sure how you can spin to be convincing through your arguments... It's a pretty indefensible position intellectually
This is actually part of a pretty valid strategy. The trick is to flood them with the conclusion - they don't need to be able to recite talking points, they just need to think "a union could be troublesome". I'd also spread stories about Union busting (not with a paper trail!) And have dozens of these posters with different, unmemorable arguments
If you convince someone "unions are bad because they have problems with corruption", they can be sat down, shown the numbers, the transparency measures, and how members could democratically boot out leadership if things go wrong. Their concern is dispelled, and if they accept the argument they're solidly on team union and distrustful of management.
If you flood them with weak arguments that make sense on the surface but fall apart if you think about them, they're left with the impression of an argument against unions. They aren't going to remember it, and if they do it'll sound like it couldn't be right to say it out loud, but they felt that way. And they're smart, so they must have been convinced by a better argument they just can't remember clearly.
This is what subliminal messaging actually looks like, this shit is evil