Yes dublinpilot, the FAA allows two pilots to log PIC. One is 'legal' PIC (in the Catalena checkout example I gave this will be the instructor) who can log it because he is
The pilot in command of an aircraft is directly responsible for, and is the final authority as to, the operation of that aircraft. (FAR 91.3)
The student can log PIC because he
Is the sole manipulator of the controls of an aircraft for which the pilot is rated or has privileges; (61.51 (e) (1) (i)
So he can log PIC because the FARs say he can. He can also log PIC if in the clouds when sole manipulator of the controls even if he doesn't have an instrument rating. He cannot be legal PIC, but he can log it.
Even if the instructor is not 'legal' PIC, he can log PIC because the FARs say he can. (FAR 61.51 (3)
What the UK is missing in the cross channel example is 61.51 (e) (1) (i) - sole manipulator of the controls.
Hope I've got all my brackets in the right places
