As the OP explains, the knives in question are not illegal and not in violation of Google's policies
They ARE in a clear violation of Google's policy which prohibits selling knives as weapons. They seem to have some confusion about the word of the ban, but as I linked elsewhere - http://support.google.com/adwordspolicy/answer/176077?hl=en
This is not at all unclear. The examples of banned knives are not the exhaustive set.
And for what it's worth, assisted opening knives are only legal by the most marginal of gray areas (that the "button" is laughably a part of the blade rather than the side handle).
It mentions several categories of knives that are legally restricted in many jurisdictions. It then goes on to say that the promotion of swords and kitchen knives is allowed. Based on the OP's claims, it appears that utility pocket knives are allowed as long as they don't have assisted opening.
It's also not clear from this page that Google has a problem with the use of adwords to sell products not banned from advertising in a store that also sells products Google refuses to advertise.
The policy is completely clear: Knives that could best be described as weapons are not allowed. People do buy knives as weapons, but it's pretty rare for people to buy swords as weapons (instead they're decorative), so that difference is completely explainable.
Knives that could best be described as weapons are not allowed.
This is completely ambiguous. There are knives marketed as having been designed with input from various figures in the martial arts world or using terms like "tactical"; it's probably reasonably to say that those are designed, or at least marketed as weapons. Kitchen knives obviously aren't intended as weapons. Every other non-decorative knife on the market falls somewhere between those two points.
Google has evidently decided that assisted opening == weapon, but does not say so on its policy page. This decision is not consistent with the marketing of most assisted opening knives, nor with the opinions of knife enthusiasts. Of course, there are probably very few objective criteria one could use to determine if a pocket-size folding knife is intended to be a weapon.
I also reiterate that it is not clear from the page that selling an item banned from advertising (an assisted opening knife) on the same website as an item advertised on adwords that is allowed to be advertised on adwords (some other kind of knife that Google doesn't consider a weapon) is against the rules. Indeed, the main point of the complaint appears to be that larger adwords customers like Amazon and Walmart are doing exactly that.
I'm sure that a certain subset of people do buy knives as weapons, but I'd be surprised if it was even on the radar of total knife ownership reasons. Most buy knives for display or utility (dive, general utility, bolo/machete, etc.).
Every one of them could be used to kill someone, just like a crowbar.
They ARE in a clear violation of Google's policy which prohibits selling knives as weapons. They seem to have some confusion about the word of the ban, but as I linked elsewhere - http://support.google.com/adwordspolicy/answer/176077?hl=en
This is not at all unclear. The examples of banned knives are not the exhaustive set.
And for what it's worth, assisted opening knives are only legal by the most marginal of gray areas (that the "button" is laughably a part of the blade rather than the side handle).