englishal, of course you can do aero's and tailwheel training. I've done it on many occasions for people doing their 1 hour flight. IMC as well. As long as I can get an idea of the competence of the person I'm sitting alongside, then frankly anything goes.
I will usually chuck in an emergency or two, but I'll generally do that on any flight.
As BEagle mentions, this is all a storm in a tea cup, there have been so few occasions where I haven't signed someones log book after the 1 hour flight that I can count them on the fingers of my hand. Apart from the two examples I've already mentioned, I've never had to refuse to sign anything as the PPL themself has realised they fall well below par and has asked for more training off their own back and acknowledged their own shortcomings.
The medical analogy is flawed because 1) there isn't a passage in LASORS saying the phrase "The function of the medical examiner is to ascertain the applicant’s physical and mental health and fitness, and interject if necessary to improve on these"
And 2) The medical examination requirements are laid down. More like a proper flight test with an examiner, where there is guidance about tolerances etc given to the examiner. Fall outside these tolerances and you can be failed, though most examiners use discretion and minor infractions are usually ignorned if the rest of the flight is of a sufficient standard.
The 1 hour training flight has no guidance other than the single statement in LASORS, a very different thing from anything an AME will do.