Could it be true? Is there any way to check if those companies actually have the real thing?
I don't think it could be true just because it's so easy to have your reserves checked, it seems like in China they would be putting people to death for doing this. That doesn't mean that some companies aren't trying it, but I don't think it's happening at the scale you seem to be insinuating. In the end though these games won't work. At some point someone will have to show their Bitcoin reserves and when companies are tasked with their leaders going to jail or having to spot buy BTC to the moon, they'll do what they're supposed to do and run the price up. This would be the type of event that would send BTC to a million. Don't fear it.
Right and I said
in this post that it depends on how regulation is set up in different countries, but I am convinced in most countries there has to be a proof of reserve and it is indeed very easy to do for Bitcoin whereas difficult to verify when it's about thin air fiat money. Numbers get checked from auditors in the case of fiat money as well, but they have other constructs and asset classes that sometimes make it difficult to come up with a true and fair view.
But there could be one back door and this is when companies are allowed to secure positions in one asset class with reserves from another asset class. They would make it overly complicated again, as it is already actually.
But if the exposure can clearly be calculated, proof of reserves is either on point or it is not. I hope it works that way.