Most and majority mean more than half, in the context of proportions.

>If there are 3 people and 2 of them have $5 each and the third has $6 it would be correct to say the third has the most money despite not having 50% + 1.

This is not an applicable example, as most is not being used to refer to the proportion of money. It is using a different definition of most, which is the top rank when ranking things by quantity.