Remember 2010 well, too well actually.
Talk about pain. To this day, I have never watched the 4th quarter of Game 7. I watched the first 3 quarters and got so nervous, I switched to some innocuous show and turned on the Gamecast on my desktop, just to look once in awhile and monitor what was going on. Celts were leading going into the 4th and sure enough, the league found a way to prevent another Laker's embarrassing loss to the Celtics in a game 7, at home no less - similar to 1969 without the preceding 10 titles, just one for this group.
Not sure if anyone remembers, but as Roy said, that 2010 team limped into the playoffs with a competitively-questionable Rasheed Wallace who needed to wake up and play with some intensity. In Game 1 vs Miami in that 1st round, the Celts started out playing as badly as they had finished the regular season. Then, Paul Pierce got knocked down in a scramble for the ball on the sideline right at Miami's bench. Garnett and Co. came to Pierce's aid, there was a slight dustup between the teams and it seemed to finally light a fire under the Celtics. They took control of that game, then the series and rolled into Cleveland for the 2nd round with momentum and intensity we had not seen much of to that point. Took out Lebron (who folded like an oily beach chair in that series), then Dwight Howard and Orlando and then the Game 7, 4th quarter disaster vs the NBA League Office and the Lakers.
You could probably add the 1969 "Miracle Celtics" to the list of teams flipping the switch. However, they played the regular season with an aging team and probably sacrificed wins in an intentional effort to be rested and focused for the playoffs. It worked.