It wouldn't be the first time that an airline pushes its engineers or pilots to operate outside the regulation to cut corners only to point the fingers at them whenever investigators start gathering around the flaming wreck...
True, that does happen, but it is often the case that pressures are just in the employee's head. How many times have you flown with pilots that are rushing to get out on time? Safety first, right? If you have an aircraft with 8 orange stickers that require heavy DDG reading and comprehension, then I think it is pretty safe to assume and EXPECT to push back a little late (especially with a two man crew). You should never rush safety sensitive tasks.
You also see crews that are afraid of taking fuel for fear of being "on a list". There are all sorts of examples were employees imagine these pressures from management, but it is all in their heads really. I have one of the lowest opinions of our leaders, but I must say, I've never felt any pressure to do something opposite from what is written in our manuals.