Not really. A round trip transatlantic flight hits you with ~0.06 to 0.1 mSv and a chest x-ray is on the order of up to ~0.02 to 0.1 mSv, so roughly similar. There's a reason x-ray techs stand behind a wall, you have a VERY small chance of DNA damage with each exposure and for most people that doesn't matter because you don't fly that often or get that many x-rays but if you do it all the time, your bound to have a high energy particle smash into the wrong part of a cell's DNA. This isn't an effect of cumulative small doses but rather rolling the same dice many times.
Most exposed are not the visitors, but the thermal bath workers.
"Workers and visitors in thermal spas are exposed to radiation from radon and short-lived daughters. Radon concentrations in the premises of a thermal bath in Budapest were investigated; high radon concentrations (up to 7.15 kBq.m-3) were found in some rooms. Bronchial dose and effective dose equivalent values were estimated for the staff and the visitors. In some cases the effective dose was about or in excess of 20 mSv annual limit for the workers. Doses for the visitors were about 4 mSv per year, but exposure of the public from radon is still outside the scope of the system of dose limitation."
And cultural references can be dramatically and wildly off.
"Plant director Bryukhanov reports no more than 3.6 roentgen, which I'm told is the equivalent of a chest x-ray, so if you're overdue for a check-up…"
– HBO Chernobyl
