It was my opinion at first in Impel Down that Jinbe only opened the door for a fishman in general to join. Hatchi was redemptive, but Jinbe was the first truly heroic fishman character, setting the precedent for similarly outstanding fishmen or fishwomen to appear at the upcoming FI. But it didn't have to necessarily be him joining if an equally good and strong character, perhaps a protege of Jinbe's, came around later on.
That changed, however, when Jinbe took charge in protecting Luffy from Akainu. He was personally invested in Luffy at that point. Before then, he was strictly an agent for the greater good, keeping Ace and WB safe and in turn protecting his home that WB had sworn to defend. That went out the window once they died, and Jinbe took the lead in Luffy's survival per Ace's push. It was the first sign that Jinbe cared about Luffy's well-being for Jinbe's personal reasons, and not simply for some altruistic cause.
It was further cemented back at Amazon Lily when Jinbe alone knocked sense into Luffy. It was perhaps Luffy's most vulnerable moment, and Jinbe was the one to personally save him once again. It's what clinched their bond that would carry on to FI, one that would be nearly impossible for another candidate to surpass at that point.