My 2004 is a manual with a 4.0 and I've push-started it...never an issue. Remember, though, that our cars are electronically fuel injected and, without electrical power, the car's fuel system will not work.
I don't know why the manual says not to push start it. The worst thing I can say about it is that it's a huge pain since the truck weighs so much. I push started a Mazda3 a few weeks ago with just me pushing it...the Ranger takes 3-4 guys pushing real hard to get enough oomph to drop the clutch and get it going and that's only if you don't have a friend with a tow strap and a truck to pull you.