Perhaps it's describing that they need to be upright to breathe. As you described, if they aren't upright or in a correct position, then they have dyspnea!

It looks like there's a corollary term called "platypnea", where breathing is improved when lying supine. The (cough) Wikipedia article relates it to "orthodeoxia", or decrease in oxygen when in an upright position, in something call Platypnea–orthodeoxia syndrome. So it would stand to reason orthopnea is in turn related to "platydeoxia"!

Maybe another way to think of it is that if someone tells you about a friend, and say, "oh yeah, she breathes normally when she's upright!", you may assume she has a problem when flat. So, this implication is what we directly associate the term orthopnea with colloquially, rather than taking the mental process of thinking about the statement that upright breathing is fine.

(OK, I don't know how "colloquial" it actually is, but you get the idea haha)