DO you honestly think that a phot of a swollen ankle taken several days after the alleged contravention would prove anything? I mean, I could overstay at a private car park and say the reason was because of this injury sustained whilst walking back to the vehicle:

Let's be realistic... unless you can evidence that the injury was sustained where you say it was and then it was enough too delay the departure and also evidence that with some kind of record, it isn't going to hold any water.
Whilst I am not saying it is not a true account of what happened, you would have to be able to convince a judge that on the balance of probability, your version of events is the most likely.
If this were to go all the way to a hearing in court, then the charge is initially going to be inflated by the operator by the addition of a fake £60-£70 debt recovery fee. Then, if a claim is made, the amount claimed will be £170 + Claim fee £35 + Fixed solicitor costs £50 + statutory interest a2 8%/annum. So, around £260.
If they discontinue or the claim is struck out, you owe nothing. If it makes it all the way to a hearing and you are unsuccessful the amount awarded is likely to be less than £260 because most judges do not allow the fake £60-£70 claimed or any statutory interest, so around £180-£190 in total. If you are successful and the judge decides that you do not owe a debt, then you pay nothing and if the claimant behaved unreasonably you can claim costs too.
You have to decide whether you are prepared to risk that for what you believe to be an unfair PCN,