What kind of data are you trying to integrate? I've deployed document management systems to finance departments before, but only to manage spreadsheets and PDFs, not the transactional data stored in a finance system. It;s a completely different model.
When MIP says that it integrates well, it means with payroll systems, CRMs and the like. I doubt that there are native integrations for a DMS. But, if you have a DBA on staff, or want to hire an integrator, it's not very difficult to do some integrating on your own, on the database back-end. I've done this in the past, setting up triggers in a Financial database that push new case numbers to a table in a DMS.
I'm doing a bit of integration with MIP at my current job, but with a custom-developed case management system, not a DMS. My primary goal is to push new billing numbers into MIP. Down the road I might pull A/P data into my system. The table structure is very logical; biggest challenge was getting my LAMP installation configured to pull data from MSSQL. The good, open source DMSes tend to be written in PHP (Knowledgetree, Alfresco).