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RAW, no. The rogue ability clearly says "even if stress and distractions would normally prevent," not other factors like "the rules say that the skill can never be Taken 10 with." You can of course rule more generously yourself - but I don't think other abilities like Steady Concentration would allow that with UMD.

Specific trumps general, and while it works with all skills in general, a skill that says "you may never take 10 with this skill" wins unless the ability would specifically say "even skills that do not allow you to take 10" (I think I remember one worded like that somewhere), or is specific to Use Magic Device like the warlock's deceive item ability.

Compare to the capstone Bard Jack of All Trades ability - "At 19th level, the bard can take 10 on any skill check, even if it is not normally allowed." That would override the UMD restriction.

While you might find rule not letting you take 10 personally stressful, I don't think that quite meets the requirement of it being stress preventing taking 10 per se. :-)