That has some truth behind it, but for the most part its not true.
Most commercially available "synthetic" oil is based off of conventional (regular) oil. Its broken down and basically "rebuilt" in a lab. Its safe to mix this type of synthetic with conventional, or switch between the two as much as you want.
The other kind of synthetic oil is REAL synthetic oil. There isn't much around, and what is around is VERY expensive. Amsoil is the only company that makes real synthetic that I'm aware of. This kind of synthetic isn't suppose to be mixed with conventional, or even conventional based synthetics. This type of oil is built in a lab from scratch. Its 100% man made, where as your normal synthetics are just modified conventional oils.
Now the reason behind the thoughts of not switching between the two is because when you drain the oil, there is still some leftover inside the engine. The only way to get ALL of the oil out is to do a complete flush.
With that being said, if you switch from Pennzoil, Castrol, Mobile, Quakerstate, etc synthetics to convention (or the other way around), you will be just fine.
A lot of automotive sales people use the line "Well you ran synthetic last time, so you have to use it every time now." to get more sales. They rope you in the first time, and make you feel like you're trapped into using it afterwards