Greg didn't comment on the 'no hospitals' thing. Even the few injuries he could make out himself where nothing he could treat himself. If John were present he might have been able to do something, but he wasn't, so there was no way around the hospital. Though Lestrade he might be able to make it so that he could take Sherlock home right afterwards. He heard Moriartys voice but kept his glance on Sherlock for a little longer, before turning to look at the madman and blink. Because Moriarty was gone. How the hell could the man be so steahtly? Or had Greg just been too distracted?
He heard his name being said and ran the last few meters left to Sherlocks side, putting his gun away and kneeling down in front of the other man. His hands hovered over the injuries he could see for a moment, then he pulled out his phone. "We are in an old warehouse, not half an hour away from Baker Street" he told him, then reached out and placed a hand on Sherlocks shoulder, to get his attention. THe man looked positively wiped out and was shivering with fatigue, it seemed. Knowing him, he might not have gotten much sleep the past few days and then this... he ought to get some rest. "Sherlock I am calling an ambulance." he informed him, not asking for his opinion on this. "I have no idea how to treat any wounds and I am just not risking it." He dialled the number on his phone and quickly explained their whereabouts and everything, before hanging up and looking around, seeing a knife on a table where Moriarty had been and, without allowing himself to think of what the knife had been meant for, proceeded to cut the ties binding Sherlock to the chair. 
He didn't move him though, just did his best to keep him remotely upright. "I promise I will get you out of the hospital as soon as they've treated you, alright?" he offered, though he already knew he wouldn't be able to fulfill that promise, should SHerlock have any too heavy injuries that would not just heal by themselves with enough rest. Which reminded him that John wasn't home to keep Sherlock from doing stupid things, so he guessed, since noone was supposed to know of this, he would have to stay and look over the detective for a while.