Understanding working of MPPT charger
I think that is 100 percent correct. Technically, the charge controller will adjust itself to extract maximum available power from the panel.
If the input voltage needs to change, the controller will change it.
But the nature of the solar panel is that MPPT voltage only changes a little bit with changing light conditions. So that is why the solar panel voltage will stay the same.
In fact, the way the charge controller probably works is by changing its duty cycle (it will be a buck converter) up and down and watching to see what effect it has on the battery charge current. It will always keep the duty cycle at the value that produces maximum charge current. And this will also result in the solar panel output voltage being relatively constant.
Note that depending on the battery state of charge, the battery may not be able to accept the maximum power available. If that happens, then the controller will no longer perform maximum power point tracking. Instead, it will extract just enough power to charge the battery according to the charge algorithm.