You may find it odd but it's what's required.
This is required by the OHSAA for all high school coaches.
Pupil Activity/Coaching Permit
A program that involves athletics, routine or regular physical activity, or health and safety considerations, as determined by the local board of education, and is supervised, directed or coached by a certified or non-certified school employee
"ODE outlines new Senate Bill 2 requirements for coaches, directors, supervisors
Under the provisions of Senate Bill 2, effective June 9, 2004, the State Board will now issue a permit, instead of a validation, to direct, supervise or coach a pupil activity program. All non-licensed individuals and licensed individuals that direct, supervise or coach a physical activity program that involves athletics, routine/regular physical activity or health and safety considerations must hold this permit. The permit is valid for three years and is renewable.
By changing the character of the validation to a permit, the legislature afforded the State Board the authority to address two important concerns. First, the bill allows a school district to employ a nonlicensed individual only if they have been granted a permit issued by the State Board. Second, the bill provides that the State Board or the Superintendent of Public Instruction, on behalf of the Board, may investigate the background of any applicant (licensed or nonlicensed) for the pupil activity program permit, in the same manner as an investigation of applicants for educator licenses and permits. This change means that for every new Pupil Activity Supervisor Permit applicant, a BCI/FBI background check must be submitted along with the application, fee and evidence of completion of successful completion of an approved first-aid program...."
Pupil Activity Permit Requirements
The Pupil Activity Permit is required for a pupil activity program that involves athletics, routine or regular physical activity or activities with health and safety considerations.
Requirements for a Pupil Activity Permit
Completion of one of the following first aid/sports injury prevention trainings:
The 6 hour fundamentals of coaching course is online at the NFHS site. When completed a certificate of completion must accompany the Pupil Activity Permit application or renewal request. The course has multiple online tests which must be passed for each respective section.
Either the High School coaches that you know in Ohio are not properly certified as required by the OHSAA or they have misinformed you.
On another note, any school having coaches active with high school sports during a scheduled contest and not being certified can be fined by the OHSAA $250 per occurrence per coach.