Train bogies can rotate around their center and follow the curves, I'd be very suprised if the actual car bent.

They don't bend, they twist. In a leftward turn, the rail tilts a bit to the left. So, when entering a leftwards bend, the front right wheel moves up a bit before the back right wheel does. That causes slight torsion in the carriage.

Springs decrease the effect, but springs in railway carriages tend to be quite stiff, as the rail shouldn't have large bumps.