In my master's thesis from 1976, I made the statement: "[In] Hoecker's (1960a) analysis of the Dallas tornado of 2 April 1957...the maximum tangential speed [76 m/sec (170mph)] and upward speed [67 m/sec (150mph)] were derived directly by tracking debris, dust particles, and cloud tags in scaled movies of that tornado, similar to the procedures used in the study reported here." Those velocity figures were taken directly from a published, peer-reviewed paper in the Monthly Weather Review, Vol. 88, pp. 167-180, titled "Wind Speed and Air Flow Patterns in the Dallas Tornado of April 2, 1957."
The statement from the source you reference above is incorrect. It appears to confuse Hoecker's correct information from the MWR with the results of Josh Wurman's Doppler On Wheels (DOW) recording of a "record high" measurement of 295mph as the strongest, most destructive F5 tornado in Oklahoma history up to that time was passing through the Bridge Creek area on its way to Moore, OK, on May 3, 1999. The significance of the "318mph" wind speed reference is due to the fact that in 1999, an F5 tornado had a wind speed estimate range of 261-318mph on the Fujita Tornado Intensity Scale (F-Scale). In several subsequent publications that I have read, the F5 range maximum estimate has been often cited in reference to this tornado rather than the actual Doppler recorded measurement (23mph lower, but certainly within a reasonable range of measurement "error"). I hope this clarification helps.