It does not state at the base level. It says choose a 1st, 2nd, or 3rd level spell... 3rd Level Cure Wounds is a 3rd Level Spell, that is it... text doesn't convey inflection, so it is actually hard to tell if someone is talking down, or if someone is simply being factual and people who are hypocrites are talking down by dismissing the valid points by calling it talking down.
When you create a Scroll or a Enspelled Item, you choose the level of the spell on it as well, you don't expend them, you just have to have them prepared. An Artificer with Cure Wounds has it Prepared at 3rd Level, even when they are out of 3rd Level Slots, because you don't choose the level when preparing it, you choose the level when casting it. The Spell Storing Device uses the Artificer's modifiers, not the wielder, so if the Artificer intended the spell they put in their Spell Storing Device to be the 3rd Level version, it is always 3rd level.
For the argument about it being always base level to be valid, it would need to state the spell is stored at its lowest level AND the number of uses would be based off the spells level, so a 1st level spell could be cast 30 times, as 2nd level spell could be cast 15 times, and a 3rd Level spell could be cast 10 times, but that is not the case. Some spells don't usually benefit from upcasting (Continual Flame is a great example, 2nd level spell with no specified upcast effect), and you might think there is no point (except, the Darkness Spell extinguishes/dispels Spells that create Light of 2nd level or lower, so a 3rd Level Continual Flame is worth casting to make a Continual Flame that won't be dispelled by the radius of a Darkness Spell). Note: It also makes it so the spell must be Action cast and not have a consumed component (so Speak with Animals is valid and so is Lightning Bolt, but Find Familiar, Identify, Counterspell, Continual Flame, Revivify, and Mass Healing Word all are not valid).
Since the Spell Storing Device doesn't explicitly forbid the higher level version of a spell being put it, nor explicitly state the spell is always cast at the lowest level, nor adjusts the number of castings. It is clear on what you can't put in it (Reaction Spells, Bonus Action Spells, 1 Minute Casting Time Spells, 1 Hour Casting Time Spells, Spells with consumed components... that is a huge amount of restrictions).