There doesn't seem to be any primary source material to back up this claim, so, as with many such internet sources, this can be taken with a large dose of salt. The best source of information on the Typhoon/Tempest family is Chris Thomas - if none of his books have been consulted chances are errors will have crept in.
This is very wrong; the elevator mass balance was modified starting September/October 1943, which largely eliminated the problem.
sources were at the end
THE HAWKER TYPHOON by Francis K. Mason, Profile Publications, 1966.
FIGHTERS OF WORLD WAR II by Charles W. Cain and Mike Jerram, Profile Publications, 1979.
FIGHTERS OF WORLD WAR II by David Donald, Metro Books, 1998. This document is basically an outline of the chapters on the Typhoon, Tempest, and Sea Fury in this book, with additions from the other sources.
BRITISH WAR PLANES OF WORLD WAR II, edited by Daniel Marsh, Airtime Publications, 1998.
I seem to remember reading that the tail problem also involved the rear wheel and engine/harmonic vibration not exclusively elevator flutter. The Typhoon had an annoying high pitched vibration which didnt go until they fitted a 4 blade prop which was towards the end of the war.
found this in wiki
A major problem, afflicting early production Typhoons in particular, was a series of structural failures leading to loss of the entire tail sections of some aircraft, mainly during high-speed dives. Eventually a combination of factors was identified, including harmonic vibration, which could quickly lead to metal fatigue, and a weak transport joint just forward of the horizontal tail unit. The loss of the tailplane of R7692 (having only 11 hours of flight recorded) on 11 August 1942, in the hands of an experienced test pilot (Seth-Smith), caused a major reassessment which concluded that the failure of the bracket holding the elevator mass balance bell crank linkage had allowed unrestrained flutter which led to structural failure of the fuselage at the transport joint.
Starting in September 1942, a steel strap was fitted internally across the rear fuselage transport joint, although this was soon superseded by Mod 286 (modification number 286), in which 20 alloy "fishplates" were riveted externally across the rear fuselage transport joint, while internally some of the rear fuselage frames were strengthened. This was a permanent measure designed to stop in-flight rear fuselage structural failures and was introduced on the production line from the 820th production aircraft; between December 1942 and March 1943, all Typhoons without Mod 286 were taken out of service and modified. Modified balance weight assemblies were fitted from May 1943. Finally the entire unit was completely replaced with a redesigned assembly from August 1944.[53]
Although these modifications reduced the numbers of Typhoons being lost due to tail assembly failure, towards the end of the Typhoon's life there were more tail failures, this time caused by a change to the undercarriage latch mechanism in late 1944; in high-speed flight the undercarriage fairings were pulled into the slipstream, creating an uneven airflow over the elevators and rudder resulting in tailplane and then rear fuselage structural failure.[53] In total 25 aircraft were lost and 23 pilots killed due to tail failures.[53] Thomas and Shores 1988, p. 20.