To be honest I'd probably just not tell them otherwise if I didn't do what they asked.
But no matter who looks after my boys I always say 'whatever gets you through the night'. Even though I have routines and healthy food is really high up on the agenda in my home with my kids - if someone else is doing me a favour by watching them I would happily accept their way of doing things. Much like 'different house, different rules.' I can't stand people sitting anywhere but at the table when eating ... So even if I'm looking after a child who normally watches TV when eating dinner - it just doesn't happen in my house.
I used to be pretty anal with DS1 though and stressed over in laws and 'my rules', I've learnt to let it go and my boys know my expectations and others differ.
So after that essay - I wouldn't make a point of doing things on purpose because I felt my way was better than the parents - I'd just do whatever made us all comfortable and got us through the day/night. Kids can behave/respond very differently with other people. If a bub was crying at my place I'd cuddle them up - even though I did CC with my own kids.