I think it's based on the (fahrt fahrt fahrt auf den) Autobahn. Now, I'm not german so I could be wrong, but here's what wikipedia says regarding speed limits on the autobahn:

Much of the system has no speed limit for some classes of vehicles.[1] However, limits are posted and enforced in areas that are urbanised, substandard, accident-prone, or under construction. On speed-unrestricted stretches, an advisory speed limit (Richtgeschwindigkeit) of 130 kilometres per hour (81 mph) applies.[2] While driving faster is not illegal in the absence of a speed limit, it can cause an increased liability in the case of a collision (which mandatory auto insurance has to cover); courts have ruled that an "ideal driver" who is exempt from absolute liability for "inevitable" tort under the law would not exceed Richtgeschwindigkeit.

So, it certainly seems there is a basis for the jokes, even if they aren't 100% historically accurate.

An Autobahn has per default no speed limit for cars, except when there is one indicated by a speed limit sign. But there are many parts on any Autobahn without speed limit signs, so in reality you can very often drive as fast as you want.

There are many opportunities to drive with 200km/h or more if you want, but often the traffic prevents going with this speed for longer than a few seconds or minutes.

About 1/3 of the Autobahn has speed limits. The other 2/3 dont have a speed limit

Plus, anyone who has traveled in South Asia or South America knows that Germany is much, much more safe to drive in than most of the rest of the world.