Yes, in a lot of situations it's true. We've experienced this more than once at different dealers over the years. As mentioned before, new sales puts everything on hold - they're priority. Even if you have a appointment for trouble shooting it's just a drop off date. Most times it might come in a week later to be looked at, if your lucky ( or you complain).
If they find or acknowledge the problem, the n st step takes place
1: is there a extended warranty - approval is needed - could takes weeks ( Been there)
2: once approved, if a part is out of stock - it could take weeks.
3: part comes in - it could take weeks to get you back in the cue for the repair.
I've found if you leave it for whatever reason, expect some kind of other damage. Been down that road. Paint damage, batteries dead, etc.
The only thing I have found up here in the great white north is getting work done in January, February. They aren't selling too good during the winter months. They tend to be more attentive to the repair end then.
I wish there was a mobile guy around here.