That means what exactly in relation to the fact that Minions exist in the game world outside of combat? Which is the point I am making.
I don't think we are in disagreement about the way Minions should generally be used in encounters. However, the way you suggested playing sort of fast and loose with minions or doing bait and switches with other related monster types, would be suspect at the least, and downright dishonest or unworkable in some cases.
I.e. It might indeed be possible to catch a Legion Devil on a errand or messenger mission and if it were engaged, there is simply no way to morph it into anything other than it is, because all Legion Devils are minions. There is no such thing as a standard version and they look entirely different physically than other demons.
Likewise, if players chased a minion out of one battle and into a building where it hid, such that it triggered a entirely new encounter, that creature should remain a minion when it is found and the new battle is begun, regardless if the players knew it was one beforehand. The DM knew and should retain consistency and regard for what these separate monsters roles are in the world.
You've missed the point. Nobody's morphing anything. The Legion Devil in your example does not suddenly bulk up or gain a more robust cardivascular system.
The Legion Devil doesn't have one hit point because he's a Legion Devil. He has one hit point because he was put into the encounter as a minion. If you are forced to let the party encounter a single Legion Devil outside of a balanced level-appropriate encounter you either:
a) Acknowledge that anything short of a solo monster caught alone by a five-PC party is toast, and let them kill him. ( in the example of the fleeing minion - how the heck does one non-solo creature count as 'an encounter'? If the creature flees to
the next encounter however... )
b) Quickly assign an arbitrary amount of hit points and let them rough him up - they'll still probably kill him in one round. (And it still doesn't count as an encounter. This is important for things like milestones.)
c) If they don't want to kill him, let them roleplay it out (possible skill challenge).
(In fact, there's an option d) where the Legion Devil is much higher level than the party, but in these cases the only solution is to drag the DM out the back and beat them senseless with a wiffle bat.

)
Option b is the only one that requires alteration to the stats in the MM, probably by giving every minion two sets of stats. I don't think the gain in this corner case is worth the confusion it would cause.
The much, MUCH simpler solution is to give minions an in-game rationale
not to wander out alone. For instance, declare that minions have a pack mentality, and strongly dislike being alone. They hang out in groups whenever at all possible.
And have their superiors recognise that minions are too incompetent to trust with anything important like carrying a message - you use a lurker or something for that. Minions are the expendable troops, the runts of the litter, the hapless fools not worth wasting proper training and equipment on. Why on earth would you trust them with an errand or a message? If you've ever watched any television (or if you grew up in any society that had minions) you would
know that a minion being sent to complete any task of importance is just going to end with their boss taking two asprin, putting an icepack on their head (or, if really evil, executing a few random conveniently-placed minions ) and sending someone competent out to do whatever the minion failed to achieve.
You're also forgetting that the only time PCs will ever encounter ANY creature in game is because the DM put it there (even if the module says there's a Blue Spotted Geeba in the room, the DM still has the option by RAW to change that, especially to adjust for party size and composition). Because of this, the DM can control where minions go, and where they can be found, and what they do if they're in a losing battle (which, by the way, is 'die fighting'). If the DM ignores the rules for how to use minions and as a result creates an odd situation, then where does the fault lie?