The condition you borrowed it in is a tricky point as you were given something that worked and returned something that didn't, so it makes you liable at some level.
Here you borrowed a car with a transmission that had only three miles left on it, so you are liable for probably about less than 1% of that $3000 bill.
In real life the car's owner would probably be vexatious enough to assert that your driving caused significantly premature breakage.
With regard to the racquet, you could probably get away with paying:
- nothing for the string as it was way beyond its useful life
- very little for the labour of the restring given that it was a cost that would soon arise
With a racquet again you've got the problem that it can be perhaps more convincingly asserted that your playing caused the string to break.
The sums are trivial so paying for the labour is not too big a stretch and it gives him a racquet that functions.
With expensive items, you'd obviously would not want to give in so easily on the point that the cost of repair is mainly their cost to bear.
In short, the person demanding payment for the string is being extremely unreasonable, but presumably in his mind you had a duty to return it in a functioning state.
He should however have made that a condition of the loan.
If I could risk a speculation on psychology: it seems that when something breaks people expect you to chip in because their favour saved you the cost of a rental.
But that misses the point of a favour: it's meant to be a cost-free gift unless you abuse it.
Hence, whatever recompense you make is in the form of a favour.
One can go a little too far with this "you have to return it in the condition your borrowed it" thing. I borrow a friend's car for the afternoon, drive three miles and the transmission goes. $3000 to replace it. Am I expected to foot the entire bill??