It depends. I broadly agree with you, but there are instances where a pilot is based (at least according to their contract) in one country, but due to the particularities of airline schedules and aircraft movements, spends very little time indeed at their “base”.
Over the course of a year I can count on a single hand the number of times I’ve flown to and from my base as opposed to starting and ending my duty in other countries. Commuting is very easy from my airport (a major European hub) and therefore I don’t live in the same country I am based in.
I pay social security in the country I am based in as their law requires, but the law of the country I commute from and live in states I must pay my taxes there - luckily they have an agreement with the country I’m based in, so it’s all legal and quite straightforward. But I had to check with a lawyer, and I would suggest anyone working for Wizzair etc. spend the money to ensure they don’t get caught out with taxes and social security....even on the allegedly low salaries that some LCCs seem to pay, it is money very well spent...