The agent may have been telling the truth when he said Butler wasn't asking for the moon, though I haven't seen Mike Lombardi lie, and Lombardi said he was asking for the moon and more, while attorneys lie for a living. Even given the agent the benefit of the doubt, I'm suspecting it had more to do with making an ultimatum, something along the lines of, "look, Malcolm still has another year left on his contract, and he's willing to take a reasonable deal. But if you don't extend him now, he's gone after 2017." The fact he was complaining about Butler not getting an extension would confirm that he doesn't understand the NFL, and particularly the Patriots operate with their players. He saw this extension as something he felt the Patriots should feel obligated to do, whereas that's not how it works.
That just isn't a standard operating procedure in the NFL for any front office. Having a team option for year 4 of an UDFA is a collectively bargained right for the team, and I don't think it would sit well with Belichick being pushed to extend a guy a year early. The fact that Butler's agent grumbled after the Gilmore deal makes me think this is the more likely story, although this is just my speculation. They rarely offer extensions, and if they do, it better be a sweetheart deal...they are risking the player will not suffer a major injury during their would-be contract year, and there is a fairly big discount necessary to essentially get a market free agency deal when you are not actually a market free agent. Look at what Gronkowski is making, way below his value, but he took the deal with two years left on his contract, hence the risk reward. On the flip side, I'm sure the Patriots wish they hadn't also extended Hernandez in 2011; look at how much money (which is the least of the damage he caused) they would have saved had they waited for him to play out his contract before deciding on his long-term future. A lot can change in a year...and always does.