The _actual_ problem, though, is more insidious. It's that the engineer then frequently accomplishes the task in the shorter time frame, and looks like a miracle worker. This reinforces the manager's intuition that the engineer is padding the time estimates and trains them to continue to behave the same way in the future. What _isn't_ apparent is what was sacrificed in order to accomplish that time schedule.
How much maintenance was deferred? How many other things had their schedules slip? These things are actual tangible sacrifices made to meet a possibly arbitrary deadline.
The other side of the coin is, maybe the deadline isn't arbitrary - maybe the Enterprise will fall into the atmosphere in the 20 minutes Kirk gives Scotty, or maybe there are auditors coming on Friday and a repair needs to be completed before then.
When dealing with other people, I try to give them the benefit of the doubt on intentions, and if I receive unexpected requests, I don't just try to provide a reasonably accurate estimate of my time, but I also ask what the driver is behind the request. Certainly they are aware of pressures that I'm not, and I also voice pressures that I am under that they aren't aware of, so that together we can determine priorities and make the right path. This also makes it much easier to communicate with the people whose projects got de-prioritized, so that everyone can be on the same page.