No, a "link to your channel" does not mean that they want you to somehow link your channel with theirs. It means they want... well, a link, a hyperlink, a URL, a URI, an address, whatever you like to call it. One that looks like this:
They need that if you're contacting them by phone because they need to know what video or videos you're actually talking about. Unless you want to give an 11-character video ID like "Nn0jReZqZQs" over the phone ("Capital N, small N, zero, small J...") to somebody whose native language is not English. They just need to know the username so they can look it up in their records and see which of your videos they've claimed.
Honestly, I can understand some skepticism, but jumping to conclusions like that isn't helping anyone.