Your drawing suggests you did park reasonably.
I would never recommend falsifying your claim, which was your original question - big risk is that they require more specific proof, find that your response is inaccurate and bending the truth. Then they will take issue and maybe refuse future insurance to you, and that will go for every other company in UK, becasue they are all networked, and they can check if you have been denied insurance.
The key point about this is taking the right decision about whether you should even risk making a claim. Even if your claim is accepted, your Insurance company doesnt have a third party insurance company to claim against. Therefore by you processing the claim through your insurance policy, they will most likely (I can't say 100% but most likely) pay up anyway, but it will be recorded as a "Policy-holder Fault" claim on your record - unless you can find a witnesses who took down registration plate details of the perpetrator.Then they can normally trace them through the DVLA computer system.
Your decision may be down to whether to claim or not:-
If you get an estimate for the repair, and the bill is not significant (maybe just over whatever your excess is? ), if so, you'd be well-advised to pay for it out of your own pocket. You should still report the incident to your insurance company, but clarify that you are doing this as a point of good practice, but that you intend to pay for the damage.
Even if you have a protected no-claims bonus, it will mean a hike in your premium next year and for some years to come. I know this from a recent experience - I know it sounds illogical (why bother protecting your NCB I asked them) but a claim will always affect future premiums.
In short, I'd only ever consider claiming on insurance, if it is many 000's of pounds worth of damage, because of the impact it has on your future premiums (for around 5 years).
So don't be misled if your Insurance company says "yes, of course we will cover the cost of your claim madam" - yes they may do, but then they don't tell you how much they will charge next year!