IMO, selfishness is the key. If you have players that will do the dirty work - like blocking, running quality routes, the little things that contribute to winning close games, you will be successful. However, if you have too high a percentage of guys who are looking to pad a NFL resume for a big $$$ day, your team will pay the price for it.
Unfortunately, Miami has had too many guys focused on getting that NFL payday instead of focusing on team goals each year. This explains the large number of early entries to the NFL draft - even though they are day 2 or 3 draft picks, some not drafted at all. Everyone wants to play as early as possible, but the key is finding guys who are willing to put in the work as underclassmen - play special teams, get some game experience during the year - so they will be ready to be called upon as starters in their junior and senior years.
Urban is a bit full of it though when it comes to players. Yes, you need to have players to be elite. You can't have the 75th rated recruiting class each season and expect to consistently be a top 10 team.