I have mixed views on the subject. In one sense, I think a company is almost obligated to use its own software if it makes sense for the company. For example, if PeopleSoft is going to market PeopleSoft Financials, it should also be using it. Otherwise, why would an external customer be interested? If PeopleSoft wasn't using its own product, it could indicate that its product is lacking.
On the other hand, the requirements that go into the software being developed by a company are not always the requirements that actual users of the system would submit. Just because a company is developing an application, doesn't mean it will meet the needs of all communities. Perhaps the application being built is great for one type of organization but not for another. In this instance, I would say that it would be a poor business decision to try to fit the process into the tool. I believe the tool should always support the process, not the other way around.