Is it possible she is giving him a bath but not washing his hair? My DH gives our DS his nighttime bath every night, but DS fights having his hair washed because he hates the water over his head. DH often gives in and lets him go a day or two before washing again. I wonder if it's the same with your MB, or do you know for sure she's not doing the bath?
Anyway, I understand your dilemma but don't think it should reflect on you. The family is just comfortable with this and you're following their wishes -- seems okay to me. I wouldn't judge you for this.
The suggestion of a hat is a good one. And if it's really filthy one day, give him a bath and then tell MB at the end of the day that you had to wash his hair because he got a ton of his lunch in it that day (in other words, make it seem like something happened that day while she was gone, not the day before).