Okay, so recently I decided I wanted to join the brotherhood of steel. I went to Boston Airport, and was directed by a soldier to the Cambridge Police Station, where I was presented with the quest "Fire Support", in which you must defeat a horde of feral ghouls which are attacking some other soldiers of the brotherhood, including Paladin Danse himself. Basically, I killed all the ghouls and went to speak to Paladin, only to be greeted with the line "Check your fire, we got hostiles", implying that there were more ghouls. I've checked pretty hard since then, and am 99.9% sure that I've killed them all.

I then decided the game had probably glitched on me, so I went to reset to my last save only to find out that my last save BEFORE killing all the ghouls was at the museum of freedom, way back when I was like, level 2 or something. I then swore loads and restarted my Xbox a billion times, all to no avail.

I have searched the internet for some kind of solution to my problem, but unfortunately the only solutions I've come across are ones which involve using console commands (not possible as I have an Xbox) or restarting to before you fought the ghouls (which I've already explained is not possible as I have no quicksaves from before I killed 'em all).

Basically, If you could come up with a solution which doesn't require console commands, a prev. quicksave or mods, I would be incredibly grateful.

Also, although I am fairly sure I killed all the ghouls, the area doesn't come up as "Cleared" on my map (I don't know if it should) and the quest itself also doesn't seem to think I've killed all the ghouls - so I dunno, maybe one got stuck in the ground somewhere?

PLS HALP - I HAVE NO IDEA WHAT TO DO

Did you finish "The Lost Patrol" prior to speaking to Danse? I just recently had the exact same problem in a game. It's the first time I've seen it. That game was also the first game I've played where I completely finished "The Lost Patrol" before I went to the police station and spoke to Danse. He gave me the same line. Perhaps it was just a coincidence, but I wonder.

In any event, it led me to delete the game. I was at level 40 and already bored to tears anyway. I'm just going to wait until the new survival mode comes out. I just hope that it's as difficult as has been suggested. Frankly, I doubt it, but we'll see.

I haven't completed the lost patrol, I assumed you had to complete "fire support" first anyway, but I think it falls under misc. quests - it doesn't matter anyway, I guess? The quest I did directly before fire support was "Reveille". I haven't completed any other BoS quests.

There are ghouls all over the place there!
Hidden away in all the buildings surrounding the square...
Plus, they look just like dead ones - until you come close to them and they 'wake up'.
Clearly you have not killed them all, even if only one remaining!
This is... unfortunate.

EDIT:
Wait - you went to the Airport, and the Prydwen was there, but...
Your last previous save was at the Museum of Freedom at Level 2?
You're joking, right?
Why do you not save your game?
You should always make a hard save whenever you level up.
If saves begin to pile up too much you can then clear out some of the older ones, or every second one, etc.

Oh yeah lol, I phrased that wrong: I had plenty of quicksaves, but they were all AFTER I had killed "all" the ghouls. The one prior to that was at the museum. Thanks anyway, I'll check the buildings and get back to you!

Actually, I see that's good news for you (IOW your game's not broken).
There's a sidestreet heading down towards the brewery to the west - watch out for the mined car carcass - infested with ghouls, and steps down to an underground entrance, etc. etc.
Lots of ghouls.
Note: I use VATS a lot, to help separate the sleeping ones from the deceased.
Don't forget to save, friend - make yourself a formal framework for doing that.