(With help from SFU computational vision professor, Brian Funt)
You are correct. More colours can be created by combining three secondary colours than by combining just the three primary colours. This is precisely why the colours of ink in inkjet printers are the secondary colours cyan, magenta and yellow, rather than red green and blue.
If you think of the colours as filters that filter out all other colours, only allowing us to see the colour they are, then the colour cyan, allows Blue and Green, but filters out Red. Similarly Magenta allows Red and Blue but cuts out Green. Yellow allows Green and Red, but eliminates Blue. Hence, secondary colours, being colours derived by adding two colours, each allow two colours to be mixed when combining, because they are each *composed* of two colours. The opposite is true for the primary colours Red, Green, and Blue. Each is made of a single colour. So you have less possible combinations when combining.