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http://leader.lds.org the Access Table shows that Bishops, Stake Presidents and Clerks (including membership) have access to the IOS. Counselors in the SP, Counselors in the Bishopric, and Executive Secretaries do not have access to the IOS.
The LDS Tool should follow this access table like the online tool. MLS access isn't a justification for access online or on the mobile tool - their security models are different (though if you were really paying attention MLS would've been modified to follow the security model approved through the President Bishopric/1st Presidency.
“A long habit of not thinking a thing wrong, gives it a superficial appearance of being right, and raises at first a formidable outcry in defense of custom.”
― Thomas Paine, Common Sense