14 CFR 251 does not require the carrier to EXPAND the carry on allowance. It only requires the airline to accept the instrument as one of the allowed carry on(s) without charging an additional fee.

On a BE fare you are allowed one personal item. That one personal item can be a small musical instrument, which meets the requirements of 14 CFR 251.3, even though the instrument may exceed the dimensions restrictions for personal items. This BE passenger would have had the choice of carrying on either her violin or her other personal item but not both. To carry on both she would have needed to have a non-BE ticket.