The issue of Public Transport is surely one of expectation. If you are seeking to be transported from A to B then you expect to do so safely and on that basis all of the AOC protection is put into place.
If you go to a flying club you must expect a slightly higher element of risk, it is not set up to public transport standards and generallly operates as a recreational activity. If you go to a flying club for a trial lesson flight or whatever you want to call it then you should be aware of that risk (albeit small). The actual content of the flight is semantics.
The person who walks into WH Smiths and buys a voucher has no concept of flying clubs or what they are about, if the did, they would save their money and go directly to the club. These people turn up with a greater expectation of a safe flight whilst an organisation who has no interest in flying, makes a lot of money out of a club activity. I would call that illegal public transport.