Seat covers in public toilets--a must for children?

[Cadmum]

My SIL was disgusted to see our DD (7) use the toilet without placing loo-roll on the seat. Am I a bad mother for having never taught her this 'trick'? I was under the impression that infection is not spread from toilet seats and that the most important part of public toilet hygiene is washing hands and avoiding touching the flushing mechanism, the tap, and the door handle once your hands are clean.

(If there are seat covers available then I encourage her to use them but I thought that the bacteria just went through the loo roll.)

DS2 doesn't even manage that. He was sent to wash his hands before piano lesson just now, came back downstairs and they were still black They clearly had not even seen water let alone soap. And he'd already eaten his tea with them like that

(Disclaimer: not my responsibility - I was still at work)