I think maybe I'm reading the question as posted here incorrectly or we've always interpreted the bonus differently.
Skill at Arms roll of 44-52 = +15 to AG modification.
If the PCs AG stats is 91, the bonus is +10
Racial Bonus of Grey Elf +5 (just picking at random)
Now add the the bonus modification from the Skill at Arms and the total bonus is +30 (10 + 5 + 15)
The AG stat itself does not go from 91 -> 106 The bonus receives the +15 modification, not the stat.
In RMCIII, the Innate Stat Abilities is based on the value of the Stat, not the stat bonus. While AG is 91, when calculating the skill totals, say for Cookery (RE/AG) you add the RE bonus (+0 Grey Elf + AG 30) / 2 = +15. Climbing is AG which = +30 bonus.
RMC-I Race Abilities chart States "Stat Bonus Modifications." The modifications from Skill at Arms/Magic apply to those stat modifications, not the value of the stat.
On the rare occasion an player rolls a 100 for a potential stat, they can opt to spend a background option to raise one stat by 2 or three stats by 1. The players inevitably opted to make the 100 stat into a 102 stat.
There are magic items they could find that would further raise their stat values even higher, but those required lengthy quests.