You could be right, it would be better to show her how to wipe herself , then she wont have to ask anyone ,I know children do not like in front of friends to ask to use the bathroom they wait ,sometimes till it is too late.
Good point about not wanting to ask the teacher for help- especially if she doesn't see other children doing that. (My 5 year old still asks to be wiped at home, too.) Perhaps she could ask to go to the nurse if she needs to poop at school. They usually have their own restroom, and maybe she would feel more comfortable asking her for help. Also, could it be that she doesn't want to take time out of what she is doing in order to go to the bathroom? Perhaps she feels like she is going to miss out on something if she leaves for that time. She knows what is going on at home, so she knows she isn't missing anything.
Could it be that she doesnt like to ask Teacher at school to go to the bathroom , many children 'hold it 'rather than ask, maybe you could check with the teacher they are given adequate times to go and told to use the bathroom, same at the friends house maybe she doesnt like to ask. It would be a good idea to start tell her to wipe herself it would give her more control about her body .Good Luck