This is a fallacy. The amount of time lost due to the puncture is more than the time he subsequently gained on Valverde. Even after the puncture, he joined the Samuel Sánchez group (who had also been dropped) and Sánchez subsequently dropped Evans and came in before him, and put in a better final time trial. If not for the puncture, then Valverde may still have won the Vuelta, and if he didn't, it would have been Sánchez that picked up the pieces, not Evans. Evans lost 1'18" to Valverde on that stage (1'26" with the 3rd place bonus seconds), and lost out by 1'32" on the GC overall. However, he lost a minute to Sammy Sánchez, who finished 37" ahead of him on the overall GC, and that was after Sánchez dropped him. Sánchez gained 4 seconds on him in the ITT.
Also, Evans spent all of week 3 sulking and didn't attack at any point, and also lost 20 more seconds to La Pandera.
Now, he might have been more motivated or put in a better showing elsewise had he not punctured, but ultimately, Sánchez proved stronger than him, limiting his losses to Sierra Nevada far better and coming in with Valverde on La Pandera.