About 18 months ago I sourced a car for a female friend, despite my best efforts had to pay full retail to get one.
Fast forward to a few weeks ago, her street has parking bays long ways both sides, someone reversed out and hit her car, a very light bumper to bumper impact that swapped some paint and slightly distorted the flimsy wing when the bumper pushed it up. I got my guy to look, he quoted 250 for cash, but gave me a written estimate for just short of 500 including VAT. She duly made a claim.
You would think when faced with a 500 quid payout and a no fuss claim they would be over the moon, but no.
They duly sent a courtesy car on a truck and wanted to take her car away for assessment, I told her to take the courtesy car but refuse them taking hers, if they refused to pay out she would never get the car back.
She did, and paid the 250 and had it repaired while she had the courtesy car.
Took about 3 weeks, all the time driving the brand new courtesy car, they paid out just short of what she paid 18 months ago, they said salvage value was 2k, she took the offer less the 2k and kept the car. The truck came and collected the courtesy car.
Bottom line is, despite being happy to settle for a 500 quid repair, the insurance company felt differently, and she has had a new car for 3 weeks, still has the car she loves and wanted, with a CAT N marker, and over 5k in her bank account.

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Absolute lunacy, moral ? Never let them take your car before paying out if you can avoid it.