Maybe she just wipes them out with kitchen roll and that would keep it oiled without the puddings sticking each week. I am sure she would take off the old bits of Yorkshire pud before putting in the new mixture!!
I love aunt bessies too, but for the time it takes for me to make them and what they turn out like (about 6" high) I prefer to have home made. Saying that, I have been known to go a while without making them.
I wash the tin foil cases mine come in for the little boy next door to take to nursery
My MIL never washes her tins though, when DH and I were there, we were helping clear up and he went to wash the yp tin and she went ballistic - it was really scary to see her so passionate about a bloody yorkshire pudding tin
We still use yp tin as shorthand for someone who is overreacting