As has been mentioned by others its your horse, so its your right to set the rules.
Also consistency is key as also already mentioned.
There are two little points i'd add though.
Firstly horses recognise people and can change their behaviour accordingly. A horse that will not lead for its owner (because he has learned that is he stops he gets mints), leads without issue for me. Similarly fields where others risk being kicked if they try to remove horses out of a set order, are no issue for me because I control all the horses. That's not to make me sound great, it just highlights how a horse doesnt have to be mouthy with anyone else just because 1 person teaches it.
Secondly, I understand why many people do not like or allow any form of mouth contact. That's probably very wise in many cases, and especially if you are new to horses. However I have also learned that mouth contact can be very powerful so I do use it with some horses. For example, if I am making contact with a new horse I will often hold my hand flat and allow them to lick or test the palm, or hold it over their muzzle. How they act tells me a lot about the horse, and also its a very strong way for them to 'smell' me.
It may be this is what your BM was also doing.
As I say not something I would encourage others to necessarily use but mouthing does not have to lead to biting, nipping or anything else if we don't wish it to.