First I'm going to use Wikipedia to disprove the statement:
Plane | T/W | Mach (max)
Concorde | 0.373 | 2.04
Typhoon | 1.15 | Mach 2 Class
F-15C | 1.07 | 2.5
Harrier | 1+ | 0.95
There will be some irregularities because most of the planes in the list are military and exact numbers may not be known. Even taking that into account, there is no correlation between thrust-to-weight ratio and max speed. This is because at max speed, aerodynamic resistance (drag) is the biggest force. This is based on aircraft design, not engine size or plane weight.
Now, what your quote was probably saying was something along the lines of "... neglecting drag, thrust to weight ratio is closely related to maximum speed"
This is backed up by this link to a NASA article on thrust to weight ratio where they make the exact same simplification of neglecting drag and talking only about horizontal acceleration.