I was a hiring manager. H1B candidates got exactly the same wage as native born. There were no differences.

I've never heard of a company giving a standard wage for a team. All the companies i've worked for (Tesla, Apple, Applied materials) give me a specific offer... Not a single person on any of my team's got paid the same. Some negotiate the base offer, some come with a higher base offer based on experience.. etc. So, based on the fact that no single US worker gets paid the same, it's very hard to imagine what you are saying is true.

Being paid the same as the other guy doesn't necessarily mean the wages themselves stayed the same. Adding H1B candidates to the talent pool exerts downward pressure on salary due to the law of supply and demand. I can't say for sure whether the allure of a green card or threat of deportation play a material factor in lowering the average salary that H1B immigrants are willing to accept. But in an environment where talent is treated as fungible (even if it isn't always so), any such downward pressure affects everyone.

When they're on visa managers know you can work them harder, especially during the PERM process

The idea is that the "same wage" you are talking about is too low to hire enough employees in the time needed that the company needed so they had to look abroad for people willing to work for that amount.

I was an H1B and this is a fucking lie.