That is absolutely true.
Back in the day, every time you made a phone call you would physically dial in the number. Usually any number you dialled frequently enough would become memorised by the repetition and you would no longer need to look in your phone book or wherever you had it written down. So it was very common to have numbers memorised for friends, family and businesses you dealt with.
With mobiles, you may only ever tap in a number once, when you save it to your contact list. There is no repetition to help you memorise it and no need to memorise it, therefore you do not memorise it.