The word "legitimacy" can mean many things. What is happening with MEW, is that the group claims to be a legitimate representation of the users of Monero (at least to a degree), based on:
1. The group members have delegated their right to express their opinions as Monero holders, to the community vote of the MEW*;
2. Joining the group is available for all as much as is practical, and the cost (if any) to join the voting body of the group is equal;
3. The group is being administered equally so that influence in the group corresponds to the ownership of XMR, and club bias does not occur;
4. Rather high percentage of all moneros outstanding are owned by the people in the group;
5. A meaningful percentage of individuals using Monero have a way to influence the group's action.
It is NOT derived from the following:
-1. rpietila or David Latapie or anyone accepts/supports it (even though they do, and are actually soon becoming founding members)
-2. the core dev team supports it (even though they probably do, at least no core dev has been specifically against MEW so far)
-3. anything else.
The criteria for legitimacy depend on what we claim to represent. Actually we believe that everyone pretty much represents himself, and the legitimacy we claim (as a group, a unity) is very small. We can only represent those members that have voted in a particular matter. (As a comparison, national parliaments claim overarching powers towards everyone, derived from much smaller actual legitimacy than MEW.)
If we are not mistaken, the core team's legitimacy statement is: "we have taken this coin to develop it, and we do what we want, and if you don't like it, you are free to sell your coins, or make a fork". There is no reason for us to obtain their blessing, as our legitimacy is based on how well we represent Monero users, and not developers. Likewise they need no blessing from us, because they exist on their own right and claim no legitimacy except over the development of the current main chain of Monero software.
* continues: "where they can express those opinions and vote for them, so that they count as much percentagewise, but are counted together with like opinions, so they have a bigger influence in the real life"