1/2 ticket a year should have never created any issue, unless all 4 tickets were received within a few months before the interview. So that case denial was definitely a IO mistake. The discussed situation is less obvious, since 9 tickets in 5 years can harldy be considered normal unless you commute in downtown NYC daily. So, I believe it may cause an issue during the interview. If denied, can it be successfully appealed? Possibly yes, but not necesserily.
Here's an interesting fact about NYC. Traffic violations issued within the city limits are under the jurisdiction of Traffic Violations Bureau, which falls under the umbrella of NYS DMV. The TVB purges its records every January 1st. Records of all tickets that were issued at least 36 months prior to the purge date are permanently deleted, as if they never existed in the first place. Let's suppose an applicant receives a ticket in July 2006, pays the fine in cash, throws out the receipt a few months later, and forgets all about it. On January 1, 2010, records of this ticket would be purged. The applicant contacts the DMV to request records of this ticket, and receives a response that no records exist. If the applicant chooses to disclose this ticket and cannot provide proof of payment and/or court disposition, and unreasonable IO (a la nyc_newbie's IO) would have a field day.
However, I would agree with you that the naturalization process is not very well formalized and relies too much on a particular IO understanding of law when it comes to grey areas.
Herein lies the root of the problem. For this very reason, the question of traffic tickets is still being discussed on this forum. I've been a member for almost 5 years, and this is probably the most frequently asked question here.