Well, that JIT will see the source code and the object code as its input and output data. So with your definition the nature of information depends not on what it is what, but on what you do to it. The role is important, specially when using it, but it is not its nature because it does not confer it with the properties that define what can be done with it. Both code and data and documentation and music, video, etc can be reproduced for free, shared, improved, audited, ported to new formats, etc.They are independent of their representation (magnetism, electrons, light...). They can be encoded in many ways and still be equivalent. Or they can be encoded in ways that lose information. But the encoding, a mapping of the different possible information items to its meaning, effects, is an external convention that is not part of that information but it is needed to use it.
But I don't know why I'm arguing with you, because I think information should be free in general, but I agree that some information needs to stay confidential, and much can be shared without being public. But once it is made available to the public it should ideally all be copyleft. Just as a general rule in an ideal world, though.