This scenario seems to have developed way beyond what I would describe as the normal syndicate "checkout" and has gone well down the training route.
I believe that a syndicate checkout completed by a non-instructor should be nothing more than a flight to confirm that the new member satisfies the syndicate requirements. Perhaps some information about some unique features of the syndicate aircraft eg specific GPS type etc etc.
However, if the new member has not flown the type before or is not current or if it is deemed that training is required then the person should be refered to an FI or CRI.
Among other things, to do otherwise leaves an gaping hole should something happen later and the "new member" complains that they were not given any "proper" training and that is why they did whatever which caused loss or injury.
Even if it is only the final part of the "training" that is done by the instructor any training needs an instructor involvement at some stage.
Finally remember that if you let them be PIC at any stage then you are happy that they can fly the aircraft safely - so why the training requirement? If you make them fly with another member who is not an instructor but will of course be PIC, then they can't log much which for most of them is a pain in the.....
Every syndicate should have access to a good friendly instructor. It is well worth it when you think of the 1 hour with an instructor requirement for all members, refreshers after the long winter lay-off, new members etc etc