Again, we don't know all the detail of what the "sick note" says or what it means in Germany.
In the UK, a "fit note" may advise you not to work, but it is not binding on employers, who only need to take it into account according to Department of Health guidelines.
The problem is that there are two parallel medical systems running (at least that's the case in the UK) i.e. the GP/NHS system and the CAA/AME system. These systems are totally disconnected and independent, and therefore do not talk to each other unless a medical practitioner in one chooses to interrogate the other by some means. It is thus very easy to hide medical conditions from a UK airline if that is what you are intent on doing.