Actually, if you read it carefully, the player was arguing that it should cost less because of that limitation - in other words, that limitation was part of the original Edge, and they were only dickering over the cost of it. You get both bonuses (the TN bonus, and NPCs have a "friendly" reaction to the character) for the 1-point Edge, but they only apply to initial contacts with an NPC.

Right I got you Glyph. Thats for the one point version. But I'm going to pay the two points for the version that works beyond initial contacts as this can help in other ways, such as making requests of contacts/buddies/etc. Paying the extra point allows for the extended use of the edge. While the book says what they finally agree on the initial form of the edge that both the GM agrees on, its only the player that wants the cheaper version. I'm going to run this by my GM and see if he feels its acceptable.