The idea that austerity during the first two years of the coalition government was vindicated by the 2013 recovery is so ludicrous that it is almost embarrassing to have to explain why. The half-truths in this case are so flimsy they do not deserve that label. I can think of two reasons why that claim could have any credibility. The first is that people confuse levels and rates or change. The second is that some critics of austerity might have occasionally overstated their case.
To see the first point, imagine that a government on a whim decided to close down half the economy for a year. That would be a crazy thing to do, and with only half as much produced everyone would be a lot poorer. However a year later when that half of the economy started up again, economic growth would be around 100%. The government could claim that this miraculous recovery vindicated its decision to close half the economy down the year before. That would be absurd, but it is a pretty good analogy with claiming that the 2013 recovery vindicated 2010 austerity.
The second point is that some critics of austerity did on a few occasions allow their rhetoric to get the better of them, and suggested that if austerity continued a recovery would never come. That was always an overstatement. It became particularly inappropriate because, as I noted in my last post, fiscal contraction did pause in 2012. But serious analysis should not be about rhetoric, or as Paul Krugman notes about passing off perception as reality. (Sometimes in my rather British way I think Paul is a little too combative with those he might have a chance to persuade, but I’m in 100% agreement with him here.)
What any knowledgeable and honest media reporting should have done is tear the vindication argument to shreds. It should have asked what contribution fiscal austerity made to the slowest recovery from a recession for centuries. That would be an honest debate. No doubt there are factors behind the delayed recovery that the government were powerless to influence, like a weak banking sector for instance. But if the banking sector is unable to support an expanding private sector, which in a recession isn’t too keen on expanding anyway, you have no business throwing public sector employees out of jobs. 
Previous posts in this series
(3) The 2007 boom
 And please, before anyone comments about how fast employment has grown, look at the data for unemployment - it went up in 2011. The deeper problems with the 'didn't we do well on employment' line will be addressed in the penultimate post in this series.