If the myopia hasn't changed much then that's not correct as myopia isn't fixed by presbyopia. Presbyopia is simply a limit on the range of focusing closer due to lens hardening and weaker muscles.
If your mother has always been myopic then she would have always been able to see well up close and closer than when wearing (non varifocal) glasses or compared to someone with perfect vision when she was not wearing glasses. However being myopic means that you can still see closer than someone with 6/6 vision once presbyopia occurs and this can give useful close vision. However mid/distance will still be affected by the myopia.
So what happens with presbyopia is the lens begins to harden as you mention. This has the effect of slightly countering myopia as you age. It will only work if your myopia is fairly low grade, and it will eventually get cancelled out — it just means you won't need readers for longer than most (say, into your 60s instead of 40s). But he is correct that your inability to see in the distance will improve somewhat while this process is ongoing.
Quite frankly, having 20/20 vision is worth it for the inconvenience of readers.
I believe my mother's myopia was only something like -1.25, so much less than my own. She says that with age she's been cured of all vision issues and has no troubles / need of correction for close up or distance.
Interestingly, key jobs in the UK military and civil aviation excluded anyone who had laser eye surgery, no matter how successful, while still taking those with uncorrected vision up to -5.0. I think that's changed recently though.
I'll admit, if contact lenses didn't exist and it was just glasses vs surgical correction, I'd be going for the latter. I truly detest glasses, but as it turns out contacts are again working well for me, and I'm living the dream of it feeling like I have nothing in my eyes / no complications / 100% vision correction, I just need to put them in in the morning and remember to take them out at night.
I think a future of matching various lenses to the climate / situations I'm in is on the cards. I'm also a keen swimmer and never understood the strict rule to not wear contacts while swimming. I wear goggles - job done. Sometimes a trickle of chlorinated water might breach the seal, but this has never been a problem for me. I think I read once that it was even inadvisable to wear contacts whilst taking a shower. I've worn contacts for 99.9% of my showers in my adult life with no issues whatsoever. All these issues sound like extended wear problems for those using lenses all day and night, including sleeping with them in, which I'd never go for.
More interesting testimony. The risks and consequences if you're one of the unlucky ones is off-the-chart life changing / ending.