It's quite clear...to me, anyway (

)...that Roddenberry intended for us to understand that humans colonized other star systems in sub-light vessels FIRST, and then discovered FTL LATER, and possibly much later. Cochrane was from Alpha Centauri and he was very much human......because Gene figured that by the mid-21st century, humans would have had colonies on our nearest stellar neighbor. No "descendant of humans transplanted by aliens" stuff is required.
True, except for a couple of details. First, it was Gene Coon, not Roddenberry, who wrote "Metamorphosis," so the idea was probably Coon's (TV writing at the time wasn't as dominated by a single showrunner as it is today). Second, they deliberately avoided pinning down a chronology when making TOS; the idea that warp drive was invented in the mid-21st century was only settled on in the TNG era, first when the 1993
Star Trek Chronology offered a conjectural date of 2061 for it, and later when
First Contact locked it down as 2063. At the time "Metamorphosis" was written, the timing hadn't been locked down. (Although for what it's worth, Coon did co-write "Space Seed," which suggested the show was 200 years or so after the 1990s; and "Metamorphosis" put Cochrane's disappearance 150 years before the episode. So Coon may have been thinking warp drive was invented in the early 21st century, for all we know.)
And third, they didn't say "Zefram Cochrane
from Alpha Centauri," but "Zefram Cochrane
of Alpha Centauri." So it's a place where he lived or a place he's associated with, not necessarily the place he was native to. Someone above offered Lawrence of Arabia as a comparison; T. E. Lawrence was born in Wales and never really lived in the Middle East, just making periodic trips there throughout his 20s, first as an archaeologist, then as a soldier during WWI. So maybe "Zefram Cochrane of Alpha Centauri" means "Zefram Cochrane, the first human being to set foot on Alpha Centauri III" or "Cochrane, the founder of the first colony at Alpha Centauri" or something like that.