For reasons others have cited, this is not only not true, it logically cannot be true. Because of how Disney operates the FP system, if FP didn't exist, those who are on the FP line and are therefore slowing down the standby line would instead be in the standby line slowing down the standby line.
Your example of how things are during EMH actually goes to prove this point. You point out that the standby line moves faster during EMH than during operating hours because there are no FP-holders slowing it down, and you point out the obvious consequence that a standby line of the same number of people takes substantially less time to navigate than it does during the day when FPs are available.
What you fail to consider is that there are a lot fewer people in the parks during EMH - which is the reason the standby lines contain the same number of people are take less time to move through. Without FP during the day,the standby line would move faster than it does as you correctly point out, but would take just as long because it would have more people on it (on average of course). Logically, there is no other possible outcome.
Actually that last bit is not completely accurate. If, as Disney seems to believe, people holding FPs are spending their time shopping instead of waiting in other lines, then the standby lines could only take longer to get through without FP. The only thing that is logically impossible is that standby waiting could be reduced by eliminating FP.