PicsinRed, neither of your claims are true. I've heard the latter one a lot and find it slightly offensive, tbh. (Naturalised German who's lived in Germany for two decades).
We're not testing anyone and everyone, but we are testing a considerably broader group of people and perhaps have a broader definition of what constitutes a contact.
Healthcare is much better resourced than in the UK (albeit not perfect and can be regionally patchy) and we pay for it via statutory insurance at around 16 % of net income (half of that if you are an employee because your employer covers the other half).
I also (controversially) think people got on board with the whole social distancing sooner. We had a cluster of cases in a particular district early on, straight after carnival, and I think how, and how fast, this spreads really sank in then and people started modifying their behaviour. I went to a concert a couple of weeks ago (before any restrictions) and the place was half-empty although I had got some of the last tickets.
Interestingly, infection rates in the areas immediately surrounding the cluster district don't really diverge from those elsewhere in Germany, which suggests that hat district did things pretty right from the outset.