Its true as you say that a fourquadrant multiplier makes an ideal mixer because it doesnt produce product frequencies  And your point that this is because it is a linear device is well taken  But I think it is important for the article to emphasize that practical mixers at radio frequencies even Gilbert cells have significant nonlinearities and produce modulation products mf  nf  And of course at microwave frequencies and above the fastestexpanding part of the radio spectrum and fastestgrowing application of mixers multiplying mixers cant be built and diode mixers are used which are nowhere near linear