I am getting mixed messages from different licenced electricians. Run length 100ft. 60 amp sub-panel in 1" conduit. Wire size according to NEC??

2 electricians have stated #6
1 electrician has stated #4
I have also verbally talked with another electrician that said you have to rate the wire based at 60deg not 90deg because the breaker says 60deg and that is the weakest link:eek:

I am starting to get confused. I don't get why there is grey in the above picture. At 1st I was thinking voltage drop, but after looking into it further this should not be a problem.
Any feedback would be good.