Is "I'm no puppeteer, Kevin" a lie?

Throughout the Devil's Advocate there are many different glimpses into John Milton's power. Despite this John tells Kevin that he's "no puppeteer", at least regarding free will. While I understand the importance of this for the ending of the movie to happen the way it does, does it not contradict some of the things we see happen through out the movie?

For example the manner in which Eddie Barzoon and Mitch Weaver die while appearing random to some extent, are clearly the result of John's power. Yet how does he achieve these without "puppeteering" and affecting free will of those directly responsible for those deaths? Another example is towards the end of the movie when Pam disappears and Kevin is left looking at an entirely empty street. A yet another example, possibly less related, is Mary Anne suddenly no longer being able to have children.

Therefore does John lie when saying he's "no puppeteer"?

If not, how is he able to achieve the things in the examples above without free will?

If yes then how is he not able to puppeteer Kevin to make him decide differently about John's offer?