Will flipping the sign of the speed of all objects in a dynamical system result in "time reversal" i.e. like rewinding a tape?

This is really a beginner question so have mercy, I was listening to a talk in astrophysics and the person said that in order to learn where a bunch of satellite galaxies were in the past "we can use the dynamics of satellites to rewind orbits backwards and trace back how they inform our picture of the local group as we see it today" or something like that.

So intuitively it seems possible. For example if I stop time as a baseball is falling, I flip the sign of its speed vector and start time again, I would expect the baseball to get back into the hand of the person who threw it.

Can this be proven mathematically, and for more complex systems involving multiple massive bodies with gravity?

What if we set the scene in micro scale, where other forces are significant?

As I was about to post the question, I looked up T-symmetry which says "Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal."

So did the speaker make a mistake? or what do you think did they meant? Or T-symmetry is not quite the same as doing the three steps (stop time, reverse speed, start time)?

I guess time-reversal is valid in certain special conditions, which galaxies satisfy over sufficiently short interval into the past (lack of friction?).