I had a reversing camera installed on one of my cars about 10 years ago, aftermarket. Needed to have the boot drilled for the camera and cable. The wire(s) needed to be fitted into the car interior itself, which may void any warranty.
My friend did it for me, with a replacement screen head unit as well. Took him a day and a half to get it fitted as he took out the side interior panels for the cables, took out the last head unit, installed the new one, etc.
Another thing to consider is that the wiring on Fords is not easy. I bought a 63 Ford Focus last December, before I got my enhanced Mobility, and I was wrongly told the car had parking sensors. Decided to just pay for it and get somebody to put them on. Guy came out and did a great job on rear sensors, but said he wouldn’t put any sensors up front. He also said Ford had the worst electrics of any manufacturer and his company refuse to do Ford sat navigation systems or anything to do with electrics up front. Fords would suddenly just stop turning on or the alarm wouldn’t activate/deactivate after installation.
Read lots of horror stories about Ford and the electrics, which is probably why Ford are reluctant to carry out the job for you. They don’t want to try to install the camera, the car just goes dead, then Ford is left holding the bag.
Reversing camera is essential to you, Motability are taking your allowance, I’d push back but I understand that it’s all a grey area with the cancellation and taking the Puma. Unless there’s protection involved in using another party to do the job, I wouldn’t. Ford are encouraging you to use somebody else not for your sake but theirs.