Etymological hint: مَحْفَظة or مِحْفَظة is a tool noun of the patter مِفْعَلة derived from حَفِظَ "to store, to protect". Fun fact: the active participle form حَافِظ means "keeper, guardian" and also "one who knows the Qur'an by heart" and thus preserves the holy text.
Actually, حفظ also means "to memorize," so a hafez of the Qur'aan can simply be understood as someboy who has "memorized" the text, no need to bring preservation into it, although there's also nothing I'm aware of that precludes your interpretation.
Which meaning came first? In other words, which meaning is an extension of the other? I would guess "to store, protect" preceded "to memorize", therefore isn't the other person's meaning really the core one with yours being derivative albeit common.