Why the requirement for a licenced (or government) aerodrome? My understanding is that this is only required for training flights for the issue or renewal of a licence or rating.
Difference training is neither of these, neither is a student flying solo after his skill test but before licence issue; as long as he does not claim the hours towards licence issue! Also, a lapsed licence flying solo before taking his skill test would only require a licenced aerodrome if the solo hours were a required part of his training. In most cases the training requirements are determined by the CFI so one could use judgement as to whether solo was required and therefore whether a licenced aerodrome was nessecary.
That's my tuppenceworth; be glad to hear your thoughts ... ...