I think it's the opposite. There's no chance at all that they'd do that because Apple would only be hurting themselves (and likely directly destroying Apple TV in some way) and the existing industry assumptions about DRM and privacy are entrenched, if not core.
We are a long ways away from when you played ball with iTunes or you didn't play digital music ball at all.
They would also likely have legal and PR pressure to exert against such a move. Regardless of whether Apple is or isn't a monopoly, they definitely don't want a billion dollar industry going after them in that angle right now.
I have lots of DRM-free games on GOG for instance. So do people I know. We've never had a single thought about pirating these. We're grown ups, we don't have time for that kind of thing.
Allowing a download doesn't _cause_ more piracy - it just makes the user have more power and control over their content they purchased.