MatterSlicer prints the skirt, then prints the base of the object, when it is finished with the object base it goes to print the base of the support on the outside. When it finished the object base it travels all the way to the other side of the bed - across the base of the object, to print the support on the outside. It seems by the time it gets to the other side the PETG has oozed out enough when it runs across the object it catches on it, and pulls it up - can't really tell if the nozzle is contacting it, or the oozed material is swipping it and catching onto it and pulling it up. As it is, i am using glue stick on heated glass, and the parts hold quite well to the bed. When it's done i have to tap it with a wrench to free them, so i don't think i can or want to glue them down any harder to the glass.
I've printed the same parts with Slic3r and they printed fine. I've never had any problems like this, so i may need to go back to Slic3r and getting the repetier firmware bed leveling to work.
I have the EXACT same issue, and this problem has destroyed several 20+ hours prints. Im going to have to switch slicers if its not fixed soon. The issue is not with bed leveling, its that sometimes the nozzle will snag onto parts when traveling across them, and z-lift eliminates this ever happening (not to mention it causes ugly streaks on top layers even if your level is spot on). Its critical to z-lift when printing support structures, or at least have an option to "Never cross printed areas when moving between islands."