I agreed with you at one time, but actually if you look at most of the recent WS champions, they did get hot in September. The '06 Cardinals are more the exception than the rule. From 2008-11, the eventual world champs had great records in September.
2005 White Sox had a near-collapse in September...they went from having a 10 game lead in the AL Central to having just a 2.5 game lead over the Cleveland Indians, who got hot in the late summer. Then they won their last 5 games of the regular season and found a second hot streak that lasted deep into October. 2005 Indians were a pretty good team, got a lot of media love and a lot of pundits were picking them to win the division, and their GM actually won GM of the year that season.
That's a decently analogous team to the 2012 Nats, as it was based on a good pitching staff and power hitting.