I don't know, this might be the actual reason... or it's just that he couldn't really put the book into film. It's very difficult to do so, some may say it's just impossible since the mediums are so different. But your answer has been used before by people defending this or that director, and sometimes it just seems like a cop out, "Oh, he didn't really care about the book".
P.S. Sorry if I sound a bit harsh. Not my intention.
Can I attempt to clarify the perceived intention of Tarkovsky with his novel adaptation? I wouldn't frame the films as evidence that he didn't care about the source material or what it attempted to say. Rather, it seems to me that these films are his responses to the novels, or at least meditations on what the novels said to Tarkovsky.
Another factor is that film and literature are very different languages, and aiming for a 1:1 translation can often result in a work that is missing pieces that were only communicable in the original.
If we acknowledge that any given novel will have aspects of it that are un-filmable (interior monologue, relative time dilation, for simple examples), then it is the job of the director to re-create the spirit of those aspects while making them work for his media. As a result, the director cannot help but inject his own views and thoughts into the work.
Nobody embodies this more strongly to me than Tarkovsky, with Kubrick as a close second. In fact, King's own attempt (shudder) at filming The Shining may prove this point all by itself; it's apparent that King doesn't understand the medium he was attempting to use.
P.S. Sorry if I sound a bit harsh. Not my intention.