I think in this analogy, it's flipped and the dirty dishes are supposed to = the toilet rolls.
Yes, That's what I meant...
Anyway, I went back to the OP because I wanted to make sure that I hadn't gotten things mixed up. It doesn't seem to be explicitly stated, but the quoted & bolded part below makes me think that it's either Marissa's job to do the dishes, or she is at least in some way responsible for the access to the disposal being blocked.
But, when the sink has stray dishes in it waiting to go into the dishwasher or even in Marissa is soaking a pan, he will leave the apple core in the sink for Marissa to take care of later.
The issue doesn't seem to be that he's not holding up his end in the kitchen, or it would be all about Why doesn't he load the dishwasher or wash the pan himself, it's that when the dishes aren't being kept up with/blocking the sink, he puts the apple core "in line" for M to deal with.
So, that's where I'm coming from when I say that I don't think anyone's "right" in this situation, and she may be doing things to annoy him just as much as he's doing things to annoy her. Very much like the TP roll situation I had quoted. (though the pillow case full of the ones he'd been squirreling away for weeks was F-U-N-N-Y!) Taking sides and declaring that one or the other of them is "right" isn't the main issue here, a helpful, loving friend would suggest that the couple communicate to each other