I'm not sure but the following link seems to indicate that's not quite right (regarding growth, that is). For example, if I understand the charts correctly the number of accepted claims was 620,488 in 1999 while in 2013 accepted claims were 884,894. If you look at applications it looks like a much bigger jump. In 1999 applications numbered 1,200,087 while in 2013, 2,640,100. That seems to indicate that the rate of acceptence to claims made has actually dropped an awful lot.
It also looks like it peaked in 2010 and 2011 as the past two years show a decrease in accepted claims.
It appears that people may be staying on disability longer though as current payment status in 2013 is almost double 1999.
Then again, termination of claims over the past couple of years seems to be increasing as well.
I dunno, make of it what you will. Here's the link:
http://www.ssa.gov/oact/STATS/dibStat.html