Total and utter tosh, needless to say, because it totally ignores your representations, which are based on boarding/alighting passengers, not parking.
Of course, because you submitted an 'informal challenge', you have received the usual Fob-Off letter that all London councils send out. They send out this nonsence because they know that almost all people, (>95%), just cough-up when they receive it, knowing nothing about the law, and glad to get the discount, and "closure" of the matter.
If you are prepared to stand you ground and take them all the way to London Tribunals you have a very strong case for cancellation of the PCN, and indeed a costs award. However you must now wait for the Notice to Owner, and submit those same representations again, and also point out in them that their reply to your informal challenge totally ignored the whole basis of your representation. You then demand that they accept that the board/alight exemption permitted you to park there and collect your aged and arthritic mother.
The NtO is sent by post to the owner of the car, using the name and address on the V5C Registration Certificate, so are you the owner, and is the address up-to-date and correct in all details.