> A PC that trains a given skill due to both race and class will be especially
> proficient with that skill.

This info is highly suspect in ADOM 1.1.1.
I have, and just did some tests that indicate that this is true. Class+race training will give you a higher skill score. However the increase-dice will be lower, as if you had pumped the skill by levelups.

Did this to illustrate just now:
Farmer class:
Human - Cooking : 15, 4d5 dice.
Hurthling - Cooking: 41, 3d5 dice.
Grey elf - Cooking:13. 4d5 dice.

Hurthling starts higher skill, but has "used up" the best dice. Grey elf raised cooking to 41, and dice became 3d5 like the hurthlings'.