To answer a few questions above...

The Safe Harbors are not legally required to disclose their own findings, or even research the validity of a notice, although in many cases it is publicly and commercially beneficial for them to do so.

One example of why it would make sense to include due diligence in researching the validity of DMCA notices is, say a business hosts marketing material for a film studio, and it includes advertising for an upcoming film. A competitor with a film that will be releasing during the same window then submits a fraudulent DMCA notice to hinder the marketing for the rival film. Immediately taking down the material would be detrimental to their business, which is why companies such as Google have implemented fraud checks. Courts have ruled that it is reasonable for them to conduct such research, so as long as it's done "expeditiously," as should the removal, should they comply. Again, that is not a clearly-defined term.

I'm sure Fandom/Wikia also recognized that the allegedly infringing material qualifies as fair use as well, as their line of business is hosting countless hordes of official content. A quick perusal of their front page contains countless images that would be suscepticle to fraudulent DCMA claims, and should a legitimate one be submitted, they wouldn't qualify for Safe Harbor, as they would clearly have form of knowledge of at least some of the material, but they and their users would clearly be protected by fair use under 17 U.S.C. § 106. Lenz v. Universal Music Corp. also requires that copyright holders do due diligence to assess fair use before submitting a notice anyway, so that was another reason why the notice was suspicious.

Safe Harbors are required to disclose certain things though. One of the conditions for qualifying as a Safe Harbor under 17 U.S.C § 512(i) is that the service provider must give explicit notice to its users of its policies regarding copyright infringement and the consequences of repeated infringing activity. Court precedent has stated that it must be "reasonably implemented" so that subscribers and account holders are informed of the terms, although they have not clearly defined what "reasonably implemented" means.

You can file a DMCA notice or counter-notice and have sufficient legal standing if you can prove that you honestly believe the material is infringing (in the former case) or that the material is non-infringing (in the latter case). Again, this is based on current court precedent, and it is the courts that decide the interpretation of the law.

The law also provides legal recourse to victims of fraudulent notices, should those users seek to claim damages from the sender of said fraudulent notices. In that situation, the Safe Harbor would be required to disclose the contact information included in the fraudulent notice to those users to satisfy the conditions in 17 U.S.C § 512(f).

I got to have a nice chat with my former entertainment law professor about this.

Also, the law isn't perfect by any means, but you guys shouldn't pick on Timmy over this. He's just doing the job he's obligated to do by his employer. If we want Wikia/Fandom to change their policies or procedures, we need to take it up with them.