I think I have heard it said( a few times) that  fhor an object entering (the EH?) of a black hole that space and time are reversed. 

Is that correct?

If that is indeed what is said then (here we go again?) is  this just saying that this is what the model does and the actual body notices no change?

As you stated that's to the perspective of the observer at infinity. The infalling observer sees no difference. The flipping of the space vs time marks a point where the mathematics breaks down into a mathematical singularity condition.

What actually happens is that the light cone of the infalling object (  Light cone - Wikipedia ) tips towards the gravitational well, and would be on its side after passing through the Event Horizon, with resulting effects on time-like and space-like motion.
Pop-sci sensationalizes this as space and time reversing, or, there is only one destination in your future.

14 hours ago, geordief said:

Is that correct?

The wording is somewhat misleading. What happens is that, once the horizon is crossed, ageing into the future always corresponds to falling down radially - in other words, you cannot maintain a constant radial position, nor can you go radially upwards, irrespective of how much downward thrust you try to exert. Even photons must always fall down. Hence, space and time enter into a relationship whereby any ageing into the future must necessarily and always lead to a decay in radial position - and since ageing into the future is inevitable, so is falling further down into the BH. Because this is a relationship between space and time, you cannot cheat your way out of this situation by trying fancy tricks of motion (like slingshotting around the singularity etc) - it doesn’t matter at all how you move, you will, on average, always fall radially downward as your clock ticks into the future.

14 hours ago, geordief said:

If that is indeed what is said then (here we go again?) is  this just saying that this is what the model does and the actual body notices no change?

If you were the free-fall body, you wouldn’t notice anything special as you fell. It’s only once you try to arrest your fall or get back out by firing thrusters, that you would notice that you are in fact unable to do so.