Three separate sections of the Guide to Advancement prohibit scout access to that list both for a) privacy worries and b) concerns that scouts will simply skip/bypass the scoutmaster or unit leader meeting (required under 22.214.171.124 The Scout, the Blue Card, and the Unit Leader) and go direct to MBCs.
The three sections are
126.96.36.199 Getting Started (“The council or district counselor list is reproduced for distribution to troops, crews, and ships. Scouts should not have access.”)
188.8.131.52 Web-Based Counselor Lists (“Scouts should not have access.”)
184.108.40.206 Unit Counselor Lists (“Due to concerns about merit badge counselor privacy, and since Scouts should receive the names and contact information from the Scoutmaster, unit counselor lists should not be made available to Scouts.”)
If he needs a MBC, the place to go is the SM/unit leader.