What evidence do you have to support this claim?

How do they manage to make the same messages appear on multiple devices? I use Signal on my phone and two other computers. Even if one of them is offline, once I go online, it will show the same messages as the other devices, even if I have already seen them on my phone. They sure aren't going to connect to my phone to pull the messages from there.

I do think there is a limit to this feature – when you connect a new device, you will not see any history on there. Only messages you receive after activating the device will show up, so it's possible they just keep track of how many active devices you have, and once a message has been retrieved by all of them, it will be deleted from the server. But that would also mean that if you don't sign out of a device before retiring it, messages COULD potentially stay on their servers forever, unless they delete them after a certain period.