They are claiming copyright over their own footage.
The phenomena at question is that of people uploading mobile phone footage of TV footage, not of their own video of the match.
I do not know what the premier league tickets say; but many venues, sports or otherwise, have limits on recording in the contact for the ticket. Realistically, most seem not to care about the iPhone clip posted to a web site; quite frankly it seems that fan clips wouldn't diminish the value of the venue's film. If I want a copy of a concert or game I buy the DVD, if available, because it is actually viewable in its entirety even if it lacks the shaking, background noise and random commentary of the iPhone version. The best model, IMHO, is the Dead, who said basically tape our concerts, trade the tapes for free, but buy our music, and other items. Seems to have worked out fine for them.