Mana Ability Oddity

[Wallycaine]

While talking about what makes something a mana ability, I was struck by the realization that Mana Echoes's triggered ability, while typically not a mana ability, can become one under the right circumstances. That struck me as odd, so I figured I'd double check my understanding to make sure I'm not missing something that disallows it. The relevant rules are:

605.1, Mana Abilities

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605.1. Some activated abilities and some triggered abilities are mana abilities, which are subject to special rules. Only abilities that meet either of the following two sets of criteria are mana abilities, regardless of what other effects they may generate or what timing restrictions (such as "Activate this ability only any time you could cast an instant") they may have.
605.1a An activated ability is a mana ability if it meets all of the following criteria: it doesn't require a target (see rule 115.6), it could add mana to a player's mana pool when it resolves, and it's not a loyalty ability. (See rule 606, "Loyalty Abilities.")
605.1b A triggered ability is a mana ability if it meets all of the following criteria: it doesn't require a target (see rule 115.6), it triggers from the resolution of an activated mana ability (see rule 605.1a) or from mana being added to a player's mana pool, and it could add mana to a player's mana pool when it resolves.

If you have Words of Wilding active, and a mana ability that draws you a card (such as Selvala, Explorer Returned or Chromatic Sphere, then you end up with a mana ability that puts a 2/2 Bear token into play. Since Mana Echoes triggers off the mana ability resolving and putting a bear token into play, it seems to me it fulfills the requirements of being a triggered mana ability in that (and only that) case. Does that seem correct? Or is there something barring a triggered ability from being a mana ability under specific circumstances, if it is typically not such a thing?

[Argus]

The trigger condition of Mana Echoes is "Whenever a creature enters the battlefield". That is neither the resolution of an activated mana ability (like Wild Growth) nor mana being added to a player's mana pool (see Caged Sun). The ability of Mana Echoes is therefore not a triggered mana ability.