The devil is always in the details.
When I looked at what's included in the PSES employment status, it does say “Contracted via temporary help services agency”. It also refers to term employees, which is, I think, often another form of contract employment.
Yes, it does include contracted out services. I'm not sure whether it's an underestimate or not. I think you'd need to look a little more carefully as it, but it does include some of those categories.
Also, one of the issues that does exist is that the budget estimates for the past year would mention, say, $40.7 billion allocated to all personnel costs and $13.2 billion of that allocated to professional and special services, a number of which would be contract workers. But it's hard then to get a breakdown of that data to really understand what's going on with the number of jobs where benefits are not...and the rate of pay, etc.