What is she comparing it to?
A solid state relay doesn't need to click, but most use a 'real' one because they are cheaper. And, no, I don't make it a habit of sitting around listening and waiting for a floor warming thermostat to turn on and off - I've not lived in a place with line voltage thermostats. And, most people probably have not heard many different ones to compare. Most thermostats in homes are 24vac, and the relay contacts don't carry much of any current, so their size is small and the sound they make is often minimal. Line voltage ones need to carry a fair amount of current, so unless solid state, will be noisier than one controlling your a/c or heating system (unless you have line voltage there, not as common). So, if the comparison is between a standard HVAC thermostat and a line voltage floor warming one, nearly any floor warming thermostat will seem noisy. Without knowing the reference and context, yes, she could be making an incorrect judgment. Apples to apples.