I'll bet you're right on that !...
I call it
"Star Trek Engineering.... Going where no man has gone before"
I'm not a plumber, but I've worked with piping and pumping systems for a good bit of my career. My "gut" tells me that my lav sink drain is a short enough run to the tank, along with a small enough flow rate, that I'd likely be ok without the air admittance device. Although there may be issues if say, dumping a pot full of water in the sink, especially given the horizontal run...... So, not great but maybe ok....
...but my kitchen sink is such a long run to the tank that it would likely be problematic without it.
If my problem continues, I think I'll remove the lav valve and plug it to see what happens. If I think about it, maybe I'll throw a 1-1/2in NPT plug into my RV project box so that I'll have one handy on my next trip....