Thank you Aurore for sharing this story. It is quite light hearted and uplifting, very good to tell to young children =D
As what everyone else has said, I also don't think one can gain enlightenment just by reciting mantras. That would be akin to telling someone "if you just believe in Me, you will go to heaven". It goes against what we learn in Dharma!
Even doing elaborate pujas with all the ritual items and costumes and beautiful offerings on a daily basis does not automatically put us on the green lane to enlightenment. If we are mean, unkind, arrogant, greedy during the times we are NOT doing pujas, then our pujas will not be effective. How could they be? The pujas I know of talk about dispelling hatred, ignorance and attachment, generating compassion, love and wisdom, clearing obstacles to our spiritual practice... so how can praying for all this be effective when we are not on our holy cushions, we do the exact opposite? Definitely the Buddhas did not teach that hypocrites can become enlightened.
Likewise, with mantras, these are words/sounds that embody the qualities/energy of the deity to which the mantra relates. For e.g. om mani padme hum, is the mantra of Avalokiteshvara. Reciting this mantra can help us increase our compassion. But if we recite it while we drown a snail with salt for fun, how effective could the mantra be?
In fact, this story clearly illustrates that if we recite mantras everyday in our human life and nothing else, it is very most probably/definitely that we will go to hell, just like the mother in the story. Once we go down to the lower realms, it is very hard for us to remember a single word of Dharma, let alone see a Buddha's image. However, the educated practitioner understood the value and workings of imprints and karmic seeds, and with genuine compassion, patiently and skilfully taught his mother how to remember and recite the mantra. Because the imprints from reciting mantras in her human life was strong enough to surface in the mother's hell life despite the environment of tremendous pain and suffering, and she had planted enough seeds of enlightenment from reciting mantras earlier, she managed to open the chance to go to Amitabha's Pure Land and ultimately gain enlightenment when she heard the clanging spoon in hell.
But it is by sheer chance that she remembered the mantra at that point in time. Perhaps the son was a highly attained practitioner and was able to give her a lot of blessings, or through clairvoyance was able to give her the right prescription to get out of hell asap.
So actually, the story is not as simple as it seems, and it is consistent with what we have been taught.