As a technical instructor doing dives routinely in the range of 200 to over 400 ft with lengths of 2 to 3 hours, I would like to know what is meant by pushing your dive computer?
I have been working as a technical instructor for over 6 years and in our dive center we run events where we will do one to two deco dives a day for up to two weeks at a time (between 40 to 70 divers at a time on an event). Dives are either normoxic (200 ft) or full tri-mix 330ft or expedition (400ft) depending on the diver's qualification. The DCS incidence is very low (maybe 1 every two years), we also have DAN joining us on many events to take doppler and ultrasonic test on divers for analysis.
All dives are done on dive computers. The thing to note is that a table has a set limit (depth and time range) thus the table can be tested for each depth and time given. Dive computers on the other hand is open as the diver can go as deep as the computer can handle the pressure and stay as long as the diver's air lasts and the computer needs to deal with it, testing that calculations is a bit harder, yet they do a very good job.
For an in depth explanation on dive computer calculations see
Dive Computers
As regard to many divers getting DCS on the first day and first dive, this is true for what I have seen on our dive boats. In most cases it is due to either buoyancy control problems, exceeding dive limits by forgetting to monitor the computer or ignoring its warning and coming up without doing the deco it asks for due to ignorance or low air problems, pfo or panicked diver due to a number of reasons (normally water in the mask or not dived in a while).