Given that, bitcoins are not property, but information
Why can't information be property?
Information is inherently free, we can make laws that make it property, but it has characteristics that property doesn't. You can keep it safe by presenting it from spreading by keeping it a secret, property on the other hand is kept safe by protecting it physically. To make Information property you have to take the meme or ownership and apply that meme to the concept of information, it is intellectually dishonest, and as the internet is highlighting somewhat impractical to enforce.
Well I can see how that argument might have some philosophical validity. But in the real world of laws and regulations, information can certainly be legally considered property. And that's all that matters.