I would actually say the opposite is true for our organisation. There is no one application with modules that would "perfectly" suit our model. The Overarching Business Strategy is important, not the IT Strategy; the waterfall method where we think we have all requirements, then we design then build, works well where you can wait a long time and the team never changes. I would think that an Agile / Scrum method where the team is small and the deliverables come in cycles would better suit our outcomes.
Given the short tenure of board, management and staff and changing environment we find ourselves in, it would be more cost affective to deliver incremental improvements rather than wait for a big bang. I agree with needing an "integrated business process management system based on a whole-of-enterprise, web-enabled relational database structure", it is just the idea that we know or can determine all requirements never happens. It is the changes to scope that costs a project in time and money. To this problem small steps with defined outcomes works more efficiently.
Chris