Michael is agreeing with Kay. Specifically, he is agreeing that "most" or "all" of "the things the papers are printing about [Michael's father]" are "not true".
Michael's statement means the same thing as "I don't think those things are true, either" or "I also don't think those things are true."
The reader will need to look at the context to figure out whether Michael is sincere. It is possible that Michael really does agree with Kay.
Many English-speaking people believe in the concept of the "little white lie." In other words, some people think it is OK to tell a lie (especially one that will not be checked, and especially if the person hearing the lie will not be worse off) to reassure someone. The example (with Michael and Kay) satisfies these criteria, so Michael might think it is OK to mislead Kay:
- Michael is being polite. Perhaps his tone and reassurance are more important than the truth of what he says.
- Kay already has an opinion about what the papers are saying.
- If Michael contradicted Kay, it might make her feel bad.
- It would be hard for Kay to check what Michael really thinks -- and if challenged, he could always say he changed his mind.
Similarly, Kay might be telling a "little white lie". She would have similar reasons. Also, many English-speaking people believe it is not nice to say bad things about other people, especially when those people are not present.
It is even possible that Kay is "gossipping" in a very subtle (and nasty) way: She could be deliberately bringing up "the things the papers are printing about [Michael's father]", while pretending to tell a "little white lie" to "protect" Michael's "feelings". Many detective stories (such as Murder, She Wrote and Columbo) use this nasty form of gossip, to try to get a suspect to say something incriminating. Columbo was popular when The Godfather was written.