There are several Chief Counsel rulings on this matter. One only has to be rated for the aircraft in which he is flying to be able to log PIC. You do NOT have to be current. 61.51(e) is the bible on this.

As for the first scenario, the old guy is the sole manipulator of the controls for which he is rated so he is legally entitled to log the flight as PIC. The flight is legal because the CFI is onboard and is qualified to act as the legal PIC. In this case, the old guy can log PIC as Sole Manipulator and the CFI can log PIC due to the fact that he is providing dual instruction.

The second scenario is almost, but not quite the same. The old guy can log PIC as Sole Manipulator, but the non CFI pilot cannot log anything because it does not fit into any of the categories of 61.51. He is there to make the flight legal because he is the only one that can be the PIC, but legally he cannot log it.

Doesn't seem fair, but that is how the reg is worded.