BJT Transconductance Decrease with Increasing Base Voltage
I agree that the (short) explanation as given in Sedra/Smith is a bit misleading. In the corresponding chapter (sinewave generation) they speak about amplitude control - which means: Output amplitude limiting for rising input amplitudes (to avoid hard-clipping effects). 

For this purpose, each oscillator needs a certain non-linearity (amplitude-dependent gain characteristics). In most cases, this is implemented using extra components (diodes, FET, light bulb, NTC, ..). However, when transistor-based oscillators are concerned, we can make use of the inherent non-linearity of BJTs: The output current cannot grow without limitations because - at the same time - the voltage drop across the collector resistor increases - thereby reducing the remaining collector-emitter voltage VCE (the momentary operational point on the load line approaches the limit VCEsat).

As a consequence, the current IC cannot follow anymore the input signal increase - and hence the instantaneous ratio g=IC/VBE reduces. (Note that both values IC and VBE are NOT DC values but momentary values). 

This is not a sudden effect but a rather "smooth" effect - and the overall gain reduction (with rising amplitudes) causes acceptable distortions (in most cases, if the excessive gain for small amplitudes was not too large).

Remark: Please note that the expression g=IC/Vt is a small-signal parameter - it is the slope of the exponential curve IC=f(VBE).