I have a Yamaha 2010 150hp 4 stroke and I had the same question - I found the following Yamaha site explains:
"Do not start the outboard out of the water. Fatal damage to the powerhead, water pump, and other internal components can occur; the water flow from the garden hose via the freshwater flush fitting won’t properly cool a running outboard." See: http://www.yamahaoutboards.com/yamaha-advantage/news/fishing-tips/boaters-log-volume-1-no-5
You can start it out of water after the fresh water is attached and turned on using the "earmuffs" or a "flush bag" -- check out yamaha's video to do this - https://www.youtube.com/watch?v=ZJaTjMOEKP0
2011 Yamaha 115 hp 4 stroke motor on my 2011 Hurricane Sun Deck 187 OB boat.
The Yamaha has two flushing procedures, one is without the engine running using the hose connector I have, they state for best results to tilt motor completely out of the water run for around 15 minutes using the hose connection and to ABSOLUTELY DO NOT RUN the motor when using the hose connection.
Then on the next page they go into flushing using the muffs and running the motor at fast idle for ten or 15 minutes.
They make no mention if both methods need to be performed.
I believe it is an either or procedure, if ones motor has the factory hose connection, use that method.
If one does not have a hose connection then use the muffs.
What is correct?
2011 Hurricane Sundeck 187 OB
2002 Sea Ray Sundancer 380