It was my understanding that McNamera directly made the decision to not chrome plate the chamber and bore of the M16 for two reasons. One for cost saving and the misconception that the rifle did not need regular cleaning to function.
It wasn't McNamara. It's understandable that his name was on the lips of every soldier of the era, after the "McNamara's Morons" debacle, but it was the nameless Army Procurements Unit that created all of the problems. Also, these problems were not always at issue in Vietnam. What it comes down to is that Remington (who had worked with Stoner on creating the 5.56mm ammunition) were having difficulties supplying enough of the IMR powder used as propellant. The Army made the decision to switch back to their historical favorite ball powder. If you are familiar with reloading you know that ball powder can be measured more quickly because it flows smoother in the powder-flow turrets that munitions manufacturers use. One downside is that ball powders are notorious for sensitive to temperature shifts, and will fire much hotter if the round has been exposed to sun and heat for long periods. When the ball powders were tested the rifles were proofed at 70,000psi, and proved acceptable. However, the port pressures were much higher in actual use because of powder instability. I'm sure you're aware of ammunition "cook-offs" once a rifle is under combat conditions. I don't believe that even a chrome bolt carrier would have saved a rifle in that situation.
EDIT: Concerning the chrome chambers it would not have been the Secretary himself but the Army Ordnance Corps that would have approved non-chromed chambers to be sent to Vietnam. I understand that Colt itself did not do the chroming operations, and so it may be that the individual companies involved may not have been able to accomplish the task properly, or that barrels were rushed into assembly before the task was completed. There is a book out on the topic concerning the subcommittee to investigate the M-16 Rifle program, but I have not been able to locate a copy.