Dear Mr. albert champion:
I'm quite certain that the MB dealer used dino oil for your oil change. Even most quickie lube places already charge at least $30-50 for synthetic oil change (up to 5 qts no-name syn only + cheap filter + labor). Remember that many MB cars require 7-9 quarts of oil, which would cost roughly 5 * 8 = $40 just for the synthetic oil (no filter, no labor yet). Mercedes OEM oil filters also cost at least 2x or 3x the cheap aftermarket filters used by quickie lube places. A synthetic oil change + new filter + labor at a MB dealer usually cost around $90-110.
BTW, your car is still quite new, so it definitely loves synthetic oil. Only very old cars may have some leaking problem with synthetic oil, especially REAL synthetic oils based on Poly-Alpha-Olefin (PAO), because PAO tends to cause seals to shrink. However, modern PAO-based synthetic oils also use a small proportion of ester in addition to PAO due to the fact that ester would counterbalance PAO's shrinking effect by actually causing seals to swell.
So stay assured that they actually did use dino oil for your oil change. Moreover, if they used synthetic oil and charge you only $47, you should call to thank for their generosity.
Cheers.
Eric