You are correct. They will specifically ask you if you are leaving Germany (for example) and will adjust the car they give you on where you are going. Also, depending on where you are going, you won't want a 5-series or E-Class due to the size of the road/alleys.
I am trying to recall what vehicles I was given on my holidays to Italy (picked up in Germany), but they weren't BMW or Mercedes. I do believe I had an Audi A4 Combi on the trip that I took my parents on a tour of Europe.
Good luck. I personally wouldn't chance taking the car into Italy if it is not allowed there. To much can happen and you are liable. I also believe there are stickers on the windscreen stating what countries the vehicle cannot go into, but I may be crazy.