The Peoples Princess

I havent seen the new Helen Mirren film about the Queen & the death of Princess Diana. But I wonder if it deals at all with the Queens reaction to Tony Blairs Peoples Princess remark?

For the Queen herself, at 21, had been given the same soubriquet:

Since it was an egalitarian, democratic era, much ingenuity was exercised
in presenting her as a peoples princess

Ben Pimlott: The Queen

Did Alistair & Tony know they were not being original - or does that 'a' make it significantly different from 'the'?