Yes, but it's not just small companies with bad processes that grow up to be big companies with terrible processes.
Sometimes, small companies with good processes turn those processes into terrible ones because they think that's what it takes to become a big company. In other words, they observe the terrible processes at big companies and emulate them.
Expense reports are a classic example. Small companies have informal procedures that are built on trust (good). Large companies have formal procedures that are built on pages and pages of policies that dictate what kinds of things can be expensed and under what conditions (terrible). It's very common for the former to turn into the latter as companies grow.