The topic specifically mentions measuring current and yes it's easy to damage a meter doing that wrong.... although probably not because of polarity as much as blowing fuses.
The old rule of thumb is to set the meter on the highest range to start with, then back down once you have some idea what the current really is. If it is high, then dont back down.
The polarity doesnt matter on most digital multimeters though, but on panel meters most often it does matter. I guess it depends on the panel meter then, if it gets damaged.