I am going from recollection of a thread on NY citations specifically, but if I recall correctly, in NY, the specific traffic law in question has to have it written in that the citation can be waived if documented correction is provided. Basically, the faulty equipment citation, in NY, does not apply globally, but only where it is specifically linked. And it is not linked to any of the bike equipment laws. So say you have tail lights, and the battery dies. You get pulled over for lacking a tail light, and can immediately replace the battery. But even though you replace it in front of the officer, you are still ticketable for riding without a light.