Here's an example of what happens when process rules over common sense - you end up with a nonsensical situation, like sending penguins through a metal detector:
Two traveling penguins from Seaworld in San Antonio went through regular airport screening at Denver International Airport recently. Here, Pat and Penny are removed from their carry-on case so they can walk through the metal detector. (Pat is the good looking one)
In that example, we see airport security staff putting two penguins through the detector. One wonders where they might have been hiding something. The folly of this particular example isn't what I'm after though. Consider software development - how many completely absurd processes do you follow because they matter to some other part of the organization? The interface with the IT department is a common point of absurdity - an engineering group always needs non-standard systems for development, testing (etc). IT quite frequently has a set of standards, and is completely unwilling to bend from them. In many cases, it's not even their fault - often times, the CEO has told the CIO to "hold the line" on costs, and clamping down on non-standard requests seems like a reasonable way to do that.
What's the upshot? The upshot is that higher management often has to resolve disputes that they have no real need to even be aware of (how many CEO's really want to get into the arcana of engineering system requirements? How many even have the technical qualifications to do anything more than pick sides?).
I see this in schools too - rather than allow teachers and administrative staff to exercise judgement, a set of ironclad policies has been imposed from on high. Presumably, this has been done to limit legal exposure. The end result is, if you send your child to school with a cough drop (or, in the case of a teenage daughter, with a Motrin) - the consequences are either a long suspension or outright expulsion.
The bottom line is, when process and rules become more important than the actual job at hand, you have a real problem. Look at how you do things at work - if there are procedures you follow that you can't understand - and that make no sense - you've stepped into the process zone.