It makes sense that it would be the initiating party. If you don't support his claim, leave the region and don't support him.
I kinda agree with your logic, but a failed TO attempt can seriously hamper following ones. If someone from another duchy goes and starts the TO before any of your men in a region that could only switch to your duchy, you wouldn't really want to let him ruin the region's sympathy for your realm.
I kinda like the idea of it being calculated by the army with the more men present.
Somewhat unrelated, but this makes me think that ducal sympathy might be an interesting stat to add to the game. Regions with high ducal loyalty and low realm loyalty would get nice stat boosts in a secession, and vice versa. Regions TOs and maintenance could run on an average of both stats. I dunno, just some crazy idea off the top of my head. More stats could just mean more maintenance, though...
