I am an integrated student who recently graduated and I can honestly say that when I graduated I would have taken any job that was offered to me with no complaints whatsoever. This was an opinion shared by most of my collegues who were more concerned about getting the money moving in the right direction than having to get in to the RHS of some shiny jet.
Those people who got a turboprop job were just as thrilled as those who got a jet job and, of course, there are those who don't have jobs yet. Not every integrated student walks straight in to a job. I don't know where this misconception stems from - that integrated students are so stuck up that they won't look at anything but Boeing or Airbus. Sorry, but in my experience that is utter rubbish. Some of the guys off my course and the course before are very happily settled flying the SF340, Q400 and a couple are indeed parachute dropping.
Of course, financially speaking many people choose to go to an integrated school because they believe there is a greater chance of landing an airline job straight away at the end of the course. Nothing wrong with that, it was my choice and I don't regret it nor will I be made to feel guilty about it.