Yup. The basic idea being, “if you off yourself and save us the trouble, we’ll continue to take care of your family.”
Also, re: Fredo’s betrayal – one of the DVD special features indicates that Fredo turned over information about the layout of the Tahoe compound. Thus, he may not have moved the drapes – he may have just told them how to get in and out and what rooms were where in the house. Maybe he thought they were going to drop a horse’s head in Mikey’s bed. 
Why would Roth and Ola (sp?) need someone as close as Fredo was to Michael to get this kind of information? Seems like they could have just approached some disaffected button man who had been in the house and around the compound.
Regarding the question, “why did Michael cut Tom Hagen out of the loop?” Based on multiple readings of the books, my impression (strictly a personal theory but it makes sense) is this: Vito had promised the Five Families that, if they all made peace, he would NOT seek vengeance for Sonny’s death. Tom was consiglieri at the time, and was also bound by that promise. Micheal planned to “pay off all debts” or something like that, including vengeance for Sonny, so therefore Tom had to be off the team. Other theories work too, but don’t (IMHO) have sufficient force of logic to explain Michael’s insistence on the matter.
In regards to Godfather Part Tree, I loved it. I thought it was considerably better than II. Definitely worth a look-see, especially if you lived through the two-pope year of 1977 and wondered what the heck was going on over there. And it even has a snippet of an Elvis Costello song in one scene if you listen close enough…Timmy
Don’t look at me – I didn’t author the DVD content… 
Maybe the Corleone button men have taken good notice of what happened to the late Don’s driver for calling in sick. Maybe Fredo figured he’d be exempt from retribution for a minor (in his mind) betrayal. Maybe the button men are all smarter than Fredo (which isn’t beyond the realm of possibility).