When people say they are "non-denominational", I think what they are saying is that they are getting away from dogmatism and doctrinal differentiation, and returning strictly to what the Bible says.
I think that their attitude is that if it is in the Scriptures, then they believe it. Some denominations deny this doctrine or that teaching, etc. I think that another term they use is "full gospel". People from all denominations who discover that the Bible has so much more depth, leave their own denomination, so they call themselves "non-denominational" as they join with others who have left their particular denominations for the say reason.
For instance, in the church I attend, there are people from every background: Catholic, Methodist, Baptist, etc. (But we don't call our selves "non-denomination". The church I attend is called "Assembly of God", and the 16 fundamental beliefs of the church are all backed by Scripture, from salvation to healing, and everything in between.)