In the case of Deoxys, I thought most sources tend to share the origin that it's a mutation of a virus or some micro-organism of extra-terrestrial origin. If that remains the case then Deoxys would still match the "Unique in Gameplay, Extremely Rare if not-Unique in story" since there isn't necessarily a planet of Deoxys; rather there could be a planet full of the original Microbe that if exposed to similar radiation/energy would also turn into a Pokemon more-or-less identical to Deoxys, but will otherwise simply exist as it is. Compared to this the UB's seem to give off the sense that in their worlds a Pokemon can simply be born as a Nihilego, Buzzwole, etc. as soon as it hatches from an egg (or however they reproduce given their alien depiction).
Maybe this is just me but I've always felt like there's been a sort of hierarchy to Legendaries in depiction and weight of capturing one, akin to how in something like the Greek Pantheon you have larger and smaller scale gods among their number (this more about structure than literal deifying since that was a topic of discussion for a bit). A sort of common factor I felt among them is how much they feel "tied" to an idea vs having a level of control or governance over it. For one example, Heatran is usually described as causing volcanic eruptions if it rampages, but it feels more that it picks a Volcano to inhabit and then could agitate it, rather than a Volcano simply emerging wherever a Heatran chooses to reside. Similarly, the Bird Trio in Gen 1 (less sure about their Galarian Counterparts) are Titans in terms of their strength with their element, but they still feel more like they are drawn to and direct it than being major causes or sources. By comparison, something like Groudon/Kyogre warps the entire climate simply by being out and about unchecked, Dialga governs the actual flow of time (vs other Time Travel subjects like Celebi which move through it but can't stop or influence the flow of time directly on the world around them outside a butterfly effect).
The main thing I'm getting into with this is that I feel it's a bit too limiting to apply the "can or cannot catch and use Legendary Pokemon as a trainer without prophecy shenanigans or such" simply to Legendaries as a broad stroke, rather than it depending very much on the Legendary Pokemon in question regardless of who the trainer is. Part of this especially in the anime's case is that there have been times where "normal" Pokemon seem to be regarded in a similar manner to how we'd think of Legendary Pokemon (my immediate example being Lucario in Movie 8, in contrast to how other Gen 4 preview mons were fairly mundane like Mime Jr. or Bonsly). The Legendary label is getting looser and a bit more iffy in some in-game cases, while in the anime several Pokemon like Heatran or Darkrai simply seem to be regarded as "extremely rare" rather than having myths and legends written about them. It's not impossible or unfathomable to brefriend or capture them, but it's still something that stands out enough to garner significant attention and expectation out of a character who has one. BG Heatran dude is a joke specifically because he's so mundane as to not even be a presence, but he is still a BG character that doesn't impact the story so it's not putting much emphasis on that detail either.
To bring this back to the Tobias thing, I think I should clarify that my issue isn't strictly him having Legendary Pokemon given the above reasons (Latios and Darkrai as portrayed in the anime fit within reason to capture/train by that standard there). The issue is that, knowing the audience is inclined to recognize Legendary Pokemon as extremely powerful compared to your average trainer's roster, it feels like a shortcut to just say "this new guy's strong enough to curbstomp Ash" to the viewer rather than have him contrast Ash's training style like his rivals tend to, or at least display inventive battling techniques like Conway. Not to say you can't do this with Legendaries either, but Tobias feels a far cry from how Legendary Pokemon being owned by main characters is USUALLY something used to delve a bit more into the history or character development of the subject mon, whereas in his case there's not a whole lot we'd lose besides (failed) fan-service if he had rolled over Ash's team with a Flygon or a Gallade or another "regular" Pokemon ace. It's just another to add to the poorly-thought-out ideas behind the character concept in Sinnoh in general.
