"But at what cost? Whilst NASA didn't have the prodigious backing of Paul Allen, it might be interesting to know how much it cost the American taxpayer to achieve this feat..."
The X-15 wasn't JUST designed to fly high though...it was also designed to fly at speeds up to Mach 6.7 to test ablative coatings for future high atmosphere and reentry vehicles, crew pressure suits etc.
I believe the Rutan thing will only (!) fly at around mach two point something...still an amazing achievement for a private venture.
As for the $10m prize, it probably wont come close to offsetting Rutan's R&D expenses, however imagine the marketing profile Scaled will gain for its other business interests and programs.
Cheers