I won't comment of the dive speeds reported for Spitfires as I have not looked at any of the test documents. However, I do have a lot of test data from dive testing of a P-47D-30 performed in 1949. Curtiss Wright was exploring propeller designs that would retain a higher degree of efficiency at high Mach. Test pilot Herb Fisher flew the entire test series, making as many as 10 dives a day. The P-47 below (by then redesignated as the F-47) attained a maximum speed of Mach 0.83 during the second dive test of 10/27/49.

This Jug had been retro-fitted with dive recovery flaps, but Fisher pulled the circuit breaker and didn't use them. The under wing stores pylons had been removed to reduce drag.
I have several data sheets graphing dive performance of some of these flights and the one below represents Fisher's 6th dive of that day.

Fisher attained Mach 0.79 during this dive.
Before he was done with the test program, Fisher made over 200 dives, all of which exceeded the AAF placcarded limits by a considerable margin. Fisher even brought along his 3 year-old son on one flight, where he attained Mach 0.78, no doubt making Herb Jr. the fastest toddler on earth for some years to come. Herb Jr wrote me and said, "I do not know if you have seen the “fastest toddler” picture, well the story is true. Here's a photo."

Anyway, my point is this: Fisher's P-47 was fitted with all manner of data recording hardware, including a mach meter and a specilized pitot tube engineered for accuracy at transonic speeds. His airspeed was also measured with a ground based radar theodolite operated by NACA personnel (identical to that which verified Yeager's flights in the XS-1). They had redundant data sources to verify speeds attained.
Fisher wrote that as he reached Mach 0.80, the aircraft began to experience a severe vibration and the torque meter monitoring the prop shaft began to display a marked oscillation in torque. At Mach 0.83 the aircraft ceased accelerating and the torque meter indicated wild fluctuations. Fisher was quite concerned that the prop shaft might fail. Upon landing, an inspection revealed no apparent damage. Fisher flew the balance of the scheduled dives, but with a Mach 0.80 limit due to the very real risk of throwing the propeller under the extreme stresses of the monumental drag rise.
My understanding is that the Spitfire reported to have reached Mach 0.9 did so AFTER the prop shaft had failed and thrown the prop, thus eliminating a significant drag factor.
My regards,
Widewing