Is it stated anywhere whether or not Mythic Companions can learn the Parma Magica? I know they technically don't have the gift, but I believe they are supposed to have something comparable.
NO, your first statement was right: they don't have the gift. But if one has, he can... but then a member of the order he should be or die.
One should not confuse Mythic Companions (who have no Gift, but get 1 free Minor Virtue, and 2 points of Virtues for every point of Flaws they take) with Gifted Companions (who have the Gift, either one free Supernatural Ability or one "opened" non-Hermetic tradition, and beyond that the normal 1:1 Virtue:Flaw ratio).
Gifted Companions can learn Parma, though they are then subjected to the "Join or Die" policy of the Order - enforced with extreme rigour, since the Order of Hermes (correctly) sees their monopoly on Magic Resistance as a key strategic advantage over rival magical societies.
Mythic Companions cannot learn Parma, but often have other means granting them Magic Resistance. This includes Mythic Companions with Might (from Nephilim, to Faeries, to Demon Children, to Magic characters); with access to appropriate Divine or Infernal powers; with True Faith, a Relic, or an appropriate "Divine-sanctioned authority" (like that of a King or a Cardinal).
Thanks to both of you for the clarification.