I'm just guessing here, but I would think he would want to stay on their good side and not make them angry. If they're angry with you, then they probably wont be talking to you. Here's my take: they tell him little tidbits of information from time to time as a courtesy/friendship, but if too much of this information is leaked before marketing has a chance to do their thing, then the source gets in trouble and possibly warned about leaking information and threatened with losing their job, which means no more courtesy leaks of tidbits.
So, I wouldn't want to make them angry either. Take what they (Lee) gives us and be thankful for it, or, the other option is nothing.
You assume it's someone in TDO who is giving Lee his information. I have no idea if it is or it is not. You further assume that TDO knows (or has a likely suspicion) of whom within TDO is revealing information to Lee. Again, I have no idea if that is or is not accurate.
Disney is well aware of who Lee is.
They know who Al Lutz and Jim Hill is too. But that doesn't mean they know who is feeding them information. Although, in Hill's case, I don't think it would be too hard for anyone with knowledge of the ins and outs of WDI to figure it out.