The limit screw should definitely be checked, the derailleur should "JUST" be able to shift onto the inside cog.
The bent derailleur hanger theory is VERY LIKELY, the things bend sometimes if you look at 'em wrong. Your pulley cage should angle slightly AWAY from your hub, yours is angling INTO your hub.
You may need to put a shim/spacer on your freehub under/inside the cassette to get it further away from your wheel to give you more clearance as well. I've had to use spacers on some of my wheels too.
I have dropout and derrailleur alignment tools (by Park, good value) to check and re-adjust dropout and hanger alignment, (they come in real handy). I've saved myself and friends headaches and money.

Note: Make sure your dropouts are aligned BEFORE you check and re-align your hanger.

Ride Well Spaced and Aligned?
Pat