IMO, the CEO misunderstands the law(so do you, but they're supposed to be the professionals).
From the BB Guidance(which in this case is a statement of the law):
Yellow lines
Badge holders may park on single or double yellow lines for up to 3 hours, but in general not where there are restrictions on loading or unloading – indicated by yellow kerb dashes and / or signs on plates. You may wish to check whether a particular local council has chosen to exempt Blue Badge holders from this restriction.
Where local schemes apply, such as those that apply in parts of central London, you should check the rules for that area. You are not entitled to park on yellow lines in off-street car parks.
You must display the Blue Badge and the blue parking clock showing the quarter hour period during which you arrived......
The 15-minute period indicated on the clock MAY NOT be assumed to be the time you parked which would have been ANY TIME between 14.45 and 14.59.
Contravention did not occur because there is no proof that you were not exempt.
