In one of my previous lives I worked for several years in recruitment and, besides working with several other operators, had flight crew on contract with RYR.
These days I'm a self-employed hotelier, my years in recruitment are a distant memory, my brain cells aren't what they were so I can't recall the UK tax legislation reference, the one bought in to particularly address self-employed IT workers, but I recall the definition of a self-employed person, despite being on contract with one or more than one companies, being that they must work from different locations and not from just one location.
OK flight crew visit maybe two, three or more locations each day of their flying duties but that isn't the point, it is where they report for duty that counts and, as I recall, RYR wouldn't appoint them a fixed base, they would 'float' between bases (because RYR were too tight to pay for crew positioning, hotac etc.) and one month may be working from Germany, another month from UK, another month from Italy etc. etc. etc.
Reading regarding this German investigation, unless the Germans can get hold of the individuals duty rosters, crew records or similar I don't see how they may determine if an individual was working from a fixed base in Germany.
One previous airline I worked for had an aircraft on wet lease with Lufthansa Cityline where the crews would position from/to UK for a week's work in Germany at a time, these crew members were operating short hauls out/in of Germany much the same as many RYR flight crew are but those crew were never expected to pay tax/SS in Germany, they were paying it in UK.
Even if the German authorities decide that Captains X, Y & Z owe them X amount in tax/SS are (Brexit) UK going to start extraditing it's nationals to Germany where said individuals may argue that they were also working from other countries such as UK and Italy and "What gives Germany the right to take tax/SS due to UK and Italy?", I mean they could make any investigation so complicated I would suggest that the German equivalent of the Crown Prosecution Service would dictate "Forget it, it's going to cost too much in public funds to continue pursuing it".
I don't think the referred to individuals have too much to worry about!