There is much more to aspiration than the epiglottis itself. I have silent aspiration, and routinely in barium swallow studies liquids end up in my lungs (not 100% but enough to cause problems). I do not have a problem with solids.

I do get aspiration pneumonia regularly when I am sick in bed with the flu or anything that prevents me from standing regularly. My body seems to eliminate most of the water etc. that gets in there, unless I am in a supine position for days.

The inability to close off the trachea completely after these treatments is common, and multifaceted. The nerves that control many of the muscles of the swallowing mechanism are permanently damaged by radiation, and this is very variable from patient to patient depending on the type of radiation, quantity of it, and location it was delivered to.

As to the epiglottis not moving, that could be the case from nerve damage, but in my case it was completely destroyed, shrunk to a tiny nub by the radiation treatments, so I have none at all. This speaks to it only being one facet of the problem. I manage through a learned process of consciously holding my breath when I drink or swallow to close the opening to the trachea. For me this is a learned ability, but in most people happens naturally because the have good sensory proprioception in the back of their mouth and throat, and their body/subconcious reflexes know they are swallowing, and it is time to close the door.

This page of the OCF web site

http://oralcancerfoundation.org/dental/e_s_issues.html

speaks to some of this though it is not about aspiration entirely.