I have just been offered the same.
I raised a support call online and then spoke to an Apple advisor on the phone. He escalated to a senior advisor and he has just phoned me back. He said it is a HARDWARE issue and my phone needs replacing. I will take it in to an Appelstore so I can test any replacement before accepting it (as I suspect the ones in-store will all be faulty as well)
An update from my Genius appointment earlier this evening.
He scanned my case notes and confirmed I needed a replacement. I asked if that would be a new retail unit but he said no it would be a refurbished unit "that might contain some recycled parts". I said that I didn't want a refurb as I was still within my 14 day return period. He went back to the notes and saw I bought it online, so he said I really needed to send it back to them for a refund.
I had overheard that they had 64GB Space Grey in stock so I asked if I could buy one of those as long as we could test it was OK first? Of course, they just needed to get it from upstairs.
Whilst we waited we chatted about the problem. The genius wondered how much I actually used the level app, to which I replied the problem also affects games, camera apps etc that rely on the level. I showed him my perfect 4S, so he tested his 5, and lo-and-behold it was out by a degree. By this point a second genius was also interested, so he tested his 5 and it was also a degree out.
The new 5S arrived and it took a couple of minutes to activate it. Meanwhile genius two had checked the store display units and quietly reported to the first genius that they were ALL showing the problem (which I knew having tested them earlier). Of course the new 5S was 2 degrees out i.e. worse than my current 5s. So I thanked them for trying and said I would get back to my support guy for what to do next.
Based on this:
1) This was genuinely news to the staff, so, assuming Apple know about this problem, they are doing a very poor job informing their support staff in the stores.
2) It looks to me like it is a widespread problem that affects the 5 as well as the 5s and 5c (I have not seen a perfect 5 they have all been at least a degree off). I can understand how new hardware can have problems, but how on earth did Apple not pick up this problem with the 5 during beta testing of iOS7 and the new level display in the compass app?
3) My 5s (which is 0 degrees long edge and one degree off short edge and when flat) is as good as any 5s, 5 or 5c that I have seen (having checked colleagues phones, display models etc). The only phone I have seen that is perfect in my 4s.
I hope talk to my support guy again tomorrow. My return deadline is next Tuesday. Im hoping they might agree to extend this from 14d to 30d, in the hope an iOS7 update fixes this. My 5s is probably as good as it gets, and if I return it I will have a long wait for another online order to appear. Having used my 4s for the last couple of days, Im missing the bigger screen and touch ID, so keeping my 5s is now looking more attractive, even with this problem.