Good innovators, carefully evaluating a business process, market or customer interaction, will have little trouble finding these "not my problem" problems. They exist at the intersection of two business processes or two vendors, neither of which wants ownership or responsibility for an exchange or an externality. These problems are out there, waiting to be solved. They are adjacencies to existing services and business models. These opportunities often exist because of business model rigidity or inflexible business processes as well.
Another reason they are often ignored or overlooked? These problems are frequently solved by the application of people or process rather than technology. In an era when everyone wants to start a virtual business and scale it quickly, there are lots of entrepreneurial opportunities where true sweat equity is still valuable. These needs aren't often glamorous, but they are real needs that customers are willing to pay to have solved.