Hi carmind,
As you say, the rules are different depending on whether it is a new claim or a transfer from DLA. In the first case the payments are backdated to the start of the claim, in the latter case the PIP payment starts 4 weeks after the decision. If there were any other system for claimants transferring, there would be the potential for overpayment of those who were in receipt of DLA during the assessment but denied PIP.
Nothing on this board constitutes legal advice - always consult a professional about specific problems