I think your interpretation of the legislation is not quite right
The "subtle difference" as you put it, is not in the part to which you refer, but rather whether or not the aircraft is being flown by a CPL/ATL and used for hire or reward.
My interpretation of the legislation is just fine, thanks.
Let's eliminate the red herring you've introduced of carriage of passengers for reward. The original poster's monicker and the fact this is the Private Flying forum are reasonable indications his interest was not in that arena.
So we're left, as I stated, with the
only requirement being
notification. You may call that implied authorisation if you like, but it is beside the point because the more than subtle difference I was addressing (and that you're ignoring) is in their phrasing: a requirement to "
seek authority". Seek means something well beyond automatic authorisation by the mere act of notification and, as I said, strongly implies the right to deny such authorisation.
We have heard before of other Police Force Special Branch officers taking a similarly incorrect view, in some cases eliminating any semantic ambiguity such as you've sought to introduce by actually telling pilots that they cannot depart until they have received an authorisation number.