The question is, was Shaw even correct that it was an invitation, and if so, did the Prometheus expedition even go to the correct world from that group of five stars? It seems obvious from the film that they were not intended to go to LV-233 simply based on what the function of that outpost was, and the film ends with Shaw going to the Engineer's real home world.
I keep trying to imagine these "contact" moments between Earth civilizations and the Engineers - what was it they were communicating (by leaving the star map)? Go here? Don't go here? We're from here? I get that maybe it wasn't an invitation, but it seems like an odd location. Maybe I missed something here, as presented in the movie, the Shaw/Holloway holographic extrapolation pointed to LV-233 - and there *were* Engineers there - just not cute, cuddly ones welcoming them with open arms. Was there a point in time when humans WOULD have been welcomed at LV-233?
ON THE SCREEN -- VISUALS OF VARIOUS DIG SITES ALL OVER THE WORLD as Shaw explains --
HOLLOWAY
These are images from archaeological digs
all over Earth. Aztec. Hopi. Inuit.
Mesopotamian. Ancient Civilizations
separated by centuries that shared no
contact with one another, and yet...
(beat; with import)
The same pictogram was discovered in
every last one of them.
NOW, THE CAVE WALL we saw at the beginning of the movie. The PICTOGRAM -- The GIANT POINTING TO THE STARS.
ON THE CREW. Rapt... but CONFUSED. MORE IMAGES -- The same PICTOGRAM at other SITES
in other forms -- Sometimes etched onto a VASE -- Here as a MURAL woven into a TAPESTRY --
HOLLOWAY
We did astrological overlays of the stars
depicted in these drawings and the only
galactic system they matched was so from
Earth, these primitive cultures couldn’t
possibly have known about it.
THE SCREEN -- GRAPHIC -- THE STAR FIELDS from the various pictograms literally FLOAT OFF of their cave walls and become 3-D REPRESENTATIONS of ACTUAL CONSTELLATIONS.
HOLLOWAY
It just so happens that system has a sun
a lot like ours. And based on our long
range scans, there seemed to be at least
one planet capable of sustaining life.
(pauses for effect)
We arrived there this morning.
THE CREW REACTS -- Where is he GOING with this? Fifield speaks up, CYNICAL --
FIFIELD
We’re here because of a map in a cave?
And before Holloway can respond, Shaw does it for him --
SHAW
Not a map. An invitation.
In Spaiht's draft, when the planet was still LV-426, Shaw interprets communication as "an invite" - while in Alien, Ripley interprets the signal as "a warning" - granted the signals weren't the same and who knows who they were intended for, but interesting insight into the story's development...

lol, I think I'm overthinking this).