Smileless,
Your example of tea at grandma's - it is phrased in a very adult point of view, a young child may not put that much value in tea at grandma's. They prefer playing with their friends, watching tv, going to park, etc.
In your scenario:
1. Grandma issues an invite for tea
2. Mother says no as they already have plans to go out
3. Mother and child end up staying home
Two quick conclusions:
1. Something may have happened that the plans to go outside are cancelled- weather related, store is closed, other party they were going to visit has cancelled, child got sick, priorities at home changed (laundry is more urgent, for example), plans are rescheduled, etc.
Life happens and young families plan on the fly and last minute - time is very scarce
2. The grandma may not accept a no for an answer without a reason - a no should be sufficient
In order to protect grandma's feelings, the mother JADEs.
A 5 year old is very happily redirected to another activity and does not act as a judge who is right or wrong (lies vs honest)
This scenario is honestly very grandma oriented - tea with grandma has the most value for grandma than anybody else involved
Mothers of young kids barely have time for a cup of tea themselves, they are lucky if they can make the tea at home and drink it while it is hot