Ok, so I'm going to be the person who says it might (might) be real...
I have this condition, among others. You don't need to be terribly hypermobile to have it. One of the first signs, when I was your dd's age, was constant joint pain with no apparent cause (it's extremely unlikely that the damage will show up on an x-ray) and injuries from seemingly trivial causes that then took months to heal. People did think I was faking it, including doctors.
Without more information (maybe you'll come back and tell us she has also tried to get out of school for broken fingernails and minor colds), but actually what you report sounds quite convincing - she has consistently reported the bad ankle for 3 months (normal for BJHS people) - and if she's lying, wouldn't she be more likely to give it up and move on to persistant headaches or something else more dramatic when she realises the ankle pain sn't working?
Also, the ankle seems fine until she has to walk to school (so she's not actually trying to get out of school, just the walking) - again consistant. I used to have terribly painful knees, but they mostly only hurt when I was doing ballet (not very advanced), and, as things got worse, as I walked.
Ankle pain is also classic for this condition, as the muscles in the arch of the foot aren't strong enough to support the person's weight, putting stress on the ankle and later on the knees and hips.
Finally, the other examples you give of her complaints are also joint pain - unless you just picked those at random from a long list of unrelated complaints.
It's worth remembering that, if she does have this condition, she's unlikely to be consistently in pain the whole time - at least not at her age. Also, it can only be diagnosed by a specialist - x-rays won't show anything, and most GPs/physios know little or nothing about it. Some people have it for decades before getting diagnosed (my father), or never get a diagnosis at all (my grandfather).
If she's been complaining of the bad ankle for this long, maybe you should push for a referral to a rheumatologist, if possible even to one of the 4 clinics in the country for BJHS/EDS (Glasgow, Leeds, Great Ormond Street and UCH in London).
Does anyone else in the family have recurrent joint pain?
Would you say she is generally untruthful?