Normally Artful's expertise in all matters Czech can be trusted; indeed Stará Turá is a town. But how could it "turn around in a circle"? Stará means old.

My wild guess at the meaning of the two verses in question is the following:

Rather the old Tura will flow uphill, than that my freedom returns.

But even when the old Tora flows uphill, my freedom won't return.

It is a topos common to all Slav folklore, in hundeds of songs, normally not speaking of freedom, but of a lost lover or one's youth. Variants of the river flowing uphill include sunken stones rising back to the surface etc. In this case, a river is the appropriate image.

Obviously, the verses are political and not as old as they are meant to sound.