God, you see some crap on here!
Every fuel injected Lyc I can recall, and yes I have flown a few over the last 40 yrs, starts (cold and hot) with the mixture in idle cut-off - by the POH.
Why? Dunno - who cares - it works!
I fly lots of different aeroplanes, mostly post-maintenance test flights. Some types I have lots of time in, some very little or little recent time, and some I have never flown before (ie Expedition 350 - look it up - there is only one in Oz).
If in doubt - do it by the book - generally works fine for me!
Dr
PS - There is an exception to every rule, and in this case it is hot starting an IO520 Bonanza with a single speed (high) fuel pump!