Swallowing liquid when a foreign object is in your trachea won't help anything
It's pretty sad that you actually had to point this out.
Ignorance. I have a narrow trachea and "choke" often while eating meat or bread.
I have to eat slow(chew up more than others) and small bites, but if I feel it getting stuck liquid does indeed help flush food done.
I've also choked bad enough that I threw up food and drink to clear airway. Many times unfortunately. Coke seems to help the most to break up food when it gets stuck.
It's a weird feeling knowing food is just beyond airway, stuck still and hard to breath, but can, and you can't do anything except drink liquid to force it up(throw up) or flush down.