Unfortunately, it is true to some extent.
Not all doctors are guilty of it, but the older generation have got used to it under communism.
it is called 'lapowka' which means backhander, lapa means "paw', it is slang for putting something in your paw
When Poland was communist lapowki were common not just in hospitals but occassionally you had to produce one in shops when things were scarce (they used to hide stuff under the counter) or to get things moving such as your application for a flat/house etc.
These habits die hard and I believe some doctors in Poland would still accept backhanders.
Pay for doctors in Poland is low.
I think people are still treated whether they have 'extra' to give or not, but a 'lapowka' gets you a better place in the queue, or ocassionally, more personal attention etc.