Does that "elimination" include the supposedly active sensors on the Reliant? It's not an unknown system, the planets are numbered and I think counting is taught at Starfleet Academy.
If it were a "known" system, then why were they there searching for a 'dead' planetary body for the Genesis Experiment?
They should have known before entering the system if there were any likely candidates.
Kinda-sorta obvious to me that the system may have been listed on the star charts, but wasn't "known" because Kirk & Spock made sure that it wouldn't be.
It's even possible that Spock had the official Star Fleet charts altered by removing Ceti Alpha V as a listing.
Which would also explain why the folks on the Reliant weren't aware of the exploded planet, they had inaccurate charts for that system.
They went in seeing just what their (altered) chart showed them.
It was also apparent that they had been searching for a suitable planet for quite awhile and were becoming a bit complacent about it due to Carol Marcus' insistence that her "Exact Requirements" be met.
So they essentially weren't at the top of their game at that point.
(as well as they weren't expecting to run into anybody)