In my experience this is untrue -- I've worked with many business processes that are very complex, and software hasn't even got involved yet.

More generally, the issue is that customers often do not understand which requirements lead to complexity, and which ones don't. If the software development relationship is transactional (and in Enterprise it usually is), then this leads to unmanaged complexity.

A lot of software (and processes) fail to have an "escape hatch" where exceptions are kicked out for manual intervention. Putting this in and then managing to the intervention rate is a decent way to manage complexity.