I heard it's actually mostly limited by your computer's hardware. Maybe moreso your router.
Having a faster internet connection isn't going to matter when it's not using the internet at all. Even if they designed it to connect to the device through the internet, your router is still going to be like "Well, actually, that device is on this network so let's just connect directly to it."
So no, internet is completely irrelevant. Its your router + hardware. Some people with decent rigs haven't had issues and I'm sure I wouldn't have either. But unfortunately this deal was not available for Canadians.
The steam link connects via WiFi if picked as well as ethernet. If it was all towards your hardware, the forgets the point of having internet connection on the link then?
Theres no way it can be related to hardware as my computer is definitely not a piece of stuff (but it's not a SLI titan x machine either). I've ran steam link before perfectly fine before i had AT&T, but since i switched to a different internet provider (i used to use time warner/spectrum) it's absolute garbage, and struggles loading big picture.
It'd be better if you actually had the steam link and not listening to heresay.
Edit to elaborate:
Yes, it does go towards hardware, because it streams DIRECTLY from your computer, as its not an OS itself. You cannot use your computer while steam link is active. But that doesn't mean that "internet is completely irrelevant" because it streams it. If internet was completely irrelevant, there'd be no point to the steam link as you could just hook up your computer to the loving TV via HDMI or whatever.