I’m actually confused by the phrase “ads”, because my understanding is that Tesla has an advertising budget of $0. I assume they’re referring to marketing materials (pamphlets, websites, etc).
The channel used to perform the advertisement and how expensive that channel is are completely irrelevant.
For example, if Tesla claims in their website that their cars can drive themselves and they can't, that's false advertising and illegal in Germany. If Tesla organizes a concert in some city somewhere, and the singer states that Tesla's cars can drive themselves and they can't, that's false advertisement.
If Tesla distributes stickers to their car owners that claim that Tesla's can drive themselves, and their car owners stick them in public bathrooms where people can see them, that is, as well, illegal advertisement, even if Tesla did not stick those stickers themselves.
The law basically requires all companies selling products in Germany to be honest about what their products can and cannot do. This is good for consumers, and good for companies doing business there, because everybody is forced to play by the same rules.
The definition of being honest and what communication means etc. are all super loose, so most companies don't risk lying about their products. There are dozens of consumer protection organizations that'll sue a company for you due to false advertisement. The main consequences for the sued company are usually damages if there are any, and mainly the fines designed to discourage false advertisement. Most of the money ends up on the tax payers accounts, so consumers are really encouraged to report these times of crimes.
But that stuff is particularly relevant for non-owners as well and thus must be judged primarily through the eyes of non-owners. It doesn't matter whether Tesla pays anyone for screen time or whatever to get their message to receptive eyeballs - these eyeballs are those of non-owners which Tesla wants to convert to Tesla owners, that's the point.
The ban in question relates to any kind of marketing material, whether it is on Tesla's website or part of advertisement billboards.
