Where has been controversy, it's been primarily about how to parse documents rather than whether to parse them during a particular piece of research.
By far and away, qualitative analysis has always been the most common method for dealing with company documents. Researchers examine the documents in a more or less formal way and look for themes, attitudes, values, whatever in a more or less systematic manner. The main problem with this method is that it opens the door to unrecognized biases and subjectivity as the project continues.
Quantitative analysis has been used much less frequently. On the one hand, it's long been recognized as a powerful method that can uncover important information that is overlooked by qualitative methods. It can also neutralize sources of biases and subjectivity. On the other hand, it has historically been very expensive and time consuming, since it requires considerable coding and categorization and scoring to generate its reports.
In a practical situation, then, the cultural analyst had to choose between a method that was relatively quick and inexpensive or one that was more difficult and expensive.
Now that situation is changing as the technology for mining "big data" becomes increasingly available to many different kinds of organizational researchers.
A good example: Adam Liptak - reporting about Supreme Court opinions - talks about a new "cottage industry of quantitative analysis of Supreme Court opinions using linguistic software."
