As TurboT has said, the "trim" they keep talking about, is the exterior trim, wether it be black or chrome, rear window is just set in urethane, and he is correct in his statement that they don't know much about car glass after 2010, it's hard to find an "old guy" who still does auto glass that would know what they are doing, as it takes a toll on the body quickly, I lasted 7 years doing auto glass before my body broke down from doing it.
Also, removal tools have come a long way over the years, chances are, they are going to cut it out with a tool called an "Equalizer", looks like a sawzall, yes, it makes glass removal easier, but be careful, because they have a tendency to get overly anxious and cut them out quick, but also end up banging the edge and scratching the hell out of the paint, and it can happen with an old style cutout knife also, you will never see it until it's too late, when you start to have rust bubbles showing around the trim, they have to be careful cutting it out, and if they do not put primer over the scratch, then bingo, all of a sudden you start having rust bubbles and rot under the trim. If I were you, and they don't like it, watch over their shoulder and make sure they don't scratch the hell out of your paint, and if they do, make sure they put primer over the scratch to avoid problems down the road. Anyone who has or has had a G body car, knows the evil monster of rust showing up around the trim over time because of the installer being in a hurry to get to the next job and not priming over the scratches that go thru the paint down to bare metal, and if you are like I am, with a 30 yr old or older toy, be anal about the work they do!!! Just my 2 cents!!!
Hope you get your glass finally installed!!!