I worked for a Not For Profit organisation where ineptitude is not only tolerated but expected. These are people who would be slaughtered in a private organisation quicker than you could say 'bleeding heart'.
So this isn't really a corporate tale, more of one about human shortcomings and passing the buck. Pretty much transferable over to the private industry world.
I worked in a small team, with two managers. Both managers were completely useless and under-performing for years. As is common for these types, they got away with this by passing the buck and lying to senior management. They blamed their staff for poor performance, we were lazy, lacking motivation, always late...yada yada. We weren't, in fact we were surviving and meeting targets in an sector where all our competitors were having their funding cut and being closed down.
Eventually, these managers had to up their lies - we were difficult (yeh, we were - we told them they were useless), hard to manage and had 'attitudinal problems' (is that even a word??) The General Manager believed them, HR stepped in, and we were all put on Performance Management. The shortsightedness of such an act escaped them, and we 'naughty' staff dutifully attended daily meetings to explain our every act to our hapless manager who didn't actually understand what it was that we were doing.
This went on for six months, the only thing we could do was laugh and wait to be fired. Eventually, the General Manager was fired and his replacement quickly cottoned on to what was happening and sacked our crapola managers. We were all taken off Performance Management, had our 'naughty files' destroyed, and given counselling for our ordeal.
If this isn't incredible enough, it turned out that the old management had been messing up reporting to our government funding body and we had actually performed 15% above what was originally thought.