That suit was prepared for Rhody - at least that's what is implied during this conversation in Iron Man 2, Randy's Donuts scene (emphasis mine):
Fury: You let your friend fly away with your suit. Now, if I didn't know better...
Tony: You don't know better. I didn't give it to him. He took it.
Fury: Whoa, whoa, whoa. He took it? You're Iron Man and he just took it? The little brother walked in there, kicked your ass and took your suit? Is that possible?
Widow: Well, according to Mr. Stark's database security guidelines, there are redundancies to prevent unauthorised usage.
Rhody is clearly an authorised user.
My reasoning here is that Tony thought he was going to die - and didn't want to let Iron Man go to waste. Who else to leave a suit to, than his best friend?
Later in the movie they (Tony and Rhodes) exchange a couple of lines about the suit, but Tony never actually attempts to take it back.
That, and also if the suit wasn't modified for a new, thinner Arc Reactor Rhody wouldn't be able to put it on without making a gigantic hole in his chest. A reason for that could be to make the suits use less power from Tony's own reactor, thus not accelerating his process of dying.