normally for LEDs, the PWM frequency is very high, in the kHz range, in order to avoid flickering. the problem with driving a SSR at high frequency is that it both creates additional heat, but also more importantly- the fact that most common SSRs are zero-crossing means that there are only 120 times per second, or once every 8.3 miliseconds, when the SSR is allowed to turn off (when the AC wave crosses zero volts).
if you are driving the SSR at 100s or kHz frequency, the extra delay caused by waiting for zero crossing can heavilly effect the proportion of on/off time (if you set 50%, it might be actually 80%, or if the PWM frequency is high enough, it will be on nearly 100% all the time).
post #3 in that "PWM show us how" thread talks about needing to lower the frequency. if you had a non zero-crossing SSR, it wouldnt matter.