What russellhltn and eblood66 said.
The documentation you are reading is for MLS and does not apply to LDS Tools.
There is a fairly extensive access table that has been approved by the appropriate councils that specifies who has read and write access to everything that is part of a membership record. What you see in Leader and Clerk Resources reflects that access. Those rights may be reviewed and adjusted (and have been in the past), but that is what we go by when determining who has access to information.
LDS Tools is a different tool designed to solve different problems. In some cases, it doesn't provide information that would be available in LCR. For example, a bishop's counselor can see in LCR whether a member has been endowed and sealed (no dates) and current priesthood office (no dates). That information is not visible in LDS Tools.
MLS is from a different era. We are working on an update to the security model in MLS that better reflects the appropriate access rights. It has been named Leader and Clerk Resources.