Sprint, to answer you question, no, in general we don't get "admin" stuff to do. Sure, you have to update your Jepps and manuals and study for PCs or recurrent from time to time, but for the most part when you leave the airport on the last day of your trip, you don't have to do anything until you come back for the first day of your next trip.
I think what Train meant about flying being a small part of the job is that on any given day, I may log 3 hours of "flight time" and have 12 hours of duty time between getting out of the hotel van in the morning and getting back in it at night. Of those 3 hours of "flight time" I may only be in the air for 2 hours, with the rest of the time sitting in line waiting to get to the runway or sitting waiting for a gate to open up. The other 9 hours of duty that aren't flight time are spent getting the plane ready, waiting for a plane, doing airport appreciation time or trying to find something good to eat despite knowing damn well there isn't anything in the airport.
And keep in mind too, my day doesn't just magically end 15 minutes after block in when I go "off duty". I've still got to hope I don't die while riding to the hotel. I have to hope the hotel actually has rooms. I have to hope my room is somewhat clean, and I have to hope that it will be quiet enough for me to be able to go to sleep. And then run the same thing in reverse in the morning to get back to start my day.
His point I think was that people talk about getting into this career because they love flying. Really the majority of my day isn't spent flying. And even when I am "flying" (don't say it Seggy) the autopilot is taking care of most stuff above 18,000 feet anyways.