The insurance company will want to establish whether this lady cycles 10 miles every day or just occasionally. If she usually cycles twice a week but gets the bus or taxi 3 times a week, then the Insurance company wont be paying for for costs that are usually incurred. Equally, if she cycles in the good weather but gets the bus in the rain, they wont pay extended costs when she wouldnt usually ride in anyway.
As I said above, and lots of others have said, the wording of the letter, if reported correctly, is wrong, but the principle of establishing the true cost of the loss is correct.
Not everyone who works in an insurance company is a cycle expert, and some people do regard 10 miles each way as a huge obstacle. What would you do if faced with a claimant who said they cycled 30 miles to work every day? You would probably think, 60 mile round trip every day, Hmmm, that sounds a bit fishy, maybe they do that occasionally but not every day, lets see so proof to support the claim. But that is because we know that 10 mile is very manageble but 30 is harder.