Questions like this come up several times a year on these forums. The two curve diameters are addressing different situations.
In a nutshell:
The locomotive (single unit) will probably not derail on O36 track. However, it may likely pull whatever it is coupled to off of the track. And the outside and inside overhang will likely strike things (for example, a switch light). So, the O36 claim is true.
The locomotive and its train will likely not derail anything on an O54 curve, but you will have to look at clearances from inside and outside the curve on a case by case basis. So, the O54 claim is also true. (See next bullet point.)
If you have a scale-length Lionel E8 coupled to scale length passenger cars, or to a heavy train, you will almost certainly need to use a wider diameter curve.
The length of the coupler on the first car next to your locomotive -- as well as whether it is truck-mounted or body-mounted -- is a factor.
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