Here is the stealthy ability. It does nothing unless you have some ability hard-coded somewhere that we don't know about (then I'm sorry I reported the bug).

<AbilityBonus InternalName="StealthyAbility">
    <AbilityBonusType>Unit_Design</AbilityBonusType>
    <AbilityBonusOption InternalName="Stealthy">
        <DisplayName>Stealthy</DisplayName>
        <Description>Monsters less likely to attack</Description>
        <Icon>Ability_Stealthy_Icon.png</Icon>
        <GameModifier>
            <Provides>Monsters less likely to attack</Provides>
        </GameModifier>
        <AdditionalTrainingTurns>8</AdditionalTrainingTurns>
        <Type>Defensive</Type>
        <AIData AIPersonality="AI_General">
            <AIPriority>5</AIPriority>
        </AIData>
    </AbilityBonusOption>
</AbilityBonus>

the bolded is the only gamemodifier this skill has.

I do not know of a unitstat or gamemodifier that will prevent monsters from attacking this unit.