What is the cost of data quality issues down the line from this system? Do those costs outweigh the benefits of using this system over some other system that actually enforces referential integrity?
Unfortunately, there are plenty of applications out there (particularly those of the "database agnostic" variety) that implement their own constraints rather than relying on the database to enforce relational integrity. They have wildly divergent levels of success in ensuring that the data they produce is reasonable-- some do it quite well, others appear to create a mishmash of crud and call it data. But all of them will create at least some invalid data.
Given that, the question becomes how much the invalid data will cost you down the line to disentangle. If you're trying to, say, track the sale of securities, any trade that doesn't tie back to a valid client is going to create a problem that has to be tracked down. If you're trying to track hours on internal project, on the other hand, it's probably merely annoying if some hours worked by individuals don't tie back to a valid project. If you're going to spend thousands of man hours cleaning up the data you've generated, a system that uses constraints is going to be vastly more cost effective. If close enough is good enough, implementing your own constraints may well be sufficient.