From the information in this video
https://www.youtube.com/watch?v=g-gspJzK6uM
it appears that they
could have landed in Medellin with ~10 min of fuel to spare IF they followed a direct approach without any delays or hold (no traffic, no weather). It was because they were placed on a holding pattern due to Viva Colombia FC8170 emergency what sealed their fate.
They probably underestimated the gravity of the situation and thought they had a few more minutes left when they initially contacted Medellin ATC. If only they had declared fuel emergency as soon as they initiated descent instead of asking for priority
AFTER being placed on a hold pattern the outcome could have been totally different.
I can understand their logic of not wanting to land to refuel in Bogota. They probably believed they had a little bit more fuel left, and they were expecting light to no traffic, what would allow them direct approach to Medellin. They knew they would be landing with with very little fuel (~15-20 min) left, but
in their minds this wasn't necessarily a "red hot" emergency. They were under time pressure (to allow the players to have a good night sleep before an important match) and the Captain / Owner wasn't eager to spend money on landing fees in Bogota (in the end it was his personal money at play).
Very unprofessional (especially for a commercial crew), but I bet many pilots have landed with less than 10 min of fuel left without declaring an emergency (and kept it secret to themselves).