I had for 15 years the dog I posted about - he could dominate anyone or anything. He never had to mark to show his territory - it WAS his territory.
But marking can be marking without being dominant towards me.
I have had my own pack and foster dogs and the only times dogs have peed in my house - with me as a mostly benevolent leader are because of -
1. Drinking lots of water and not pottying when they were outside because they were busy playing, sniffing, etc. (oh, that's crazy - peeing because you have to pee bad and can't open a door because you have no thumbs!)
2. UTI - not always diagnosed on first urine sample (you also need to check blood)
5. Covering another dog's pee (in my example) not as dominance, just oh, here, that doesn't smell quite right, now that smells good
If my dogs have some kind of hidden take over the house agenda, I haven't stumbled on to it. My dogs are not for a beginner either.
My guess is if they do have a plan, it's going to be about food more than urine!
Definitely look at the situation. Take away that frame of thought and look at it clearly.