A disagreement over the PostgreSQL trademark

There are multiple types of trademark, and there are multiple ways to infringe. Trademark dilution is only one of the ways that infringment can occur. It is, as you said, when the trademark is used in a completely different industry than the original, but when the original is so big that it is in the public mind. This isn't even stuff like Coke t-shirts: since Coke does, in fact, sell t-shirts, using their logo in your own would be traditonal infrigment. Dilution is just any appearance of the mark in a way that harms the brand (other than nominative usage: a news article about Coke being made with the blood of innocents can use the logo without trademark infringment, though libel is possible if the article didn't actually uncover any innocents). For instance, if an actor in an adult film is wearing Nike shoes, that is dilution: unlike with traditional infringment, you don't need to show confusion.

Any (and I mean ANY) use of your trademark on a product similar to that provided by you MUST be sued as infringment. That is because the core purpose of a trademark is to uniquely identify a product as coming from a specific location. If a customer looks at a product, and incorrectly decides that it is yours, then you are required to sue the creator of that product. If you tolerate such products, then you lose the trademark: products with the mark can no longer be associated with you anyways, so there is no point in giving you the ability to control who has the mark.

This isn't limited to the exact list of offerings by your company (though it is more limited than the dilution): for instance, if I open a store that repairs New Balance shoes, I can't advertise myself as a "New Balance Repair Store", even though New Balance is a brand far smaller than the giants that dilution would apply to. "New Balance Health and Wellness" shop would not infringe, however: "new balance" is an english phrase, and so it doesn't get the same protections as other, more unique phrases (such as Kodak).

In this case especially, there is an obligation to sue in order to maintain the trademark. A reasonable person would conclude that a company entitled "PostgreSQL Services" (as opposed to one that simply advertises such an offering) is either offically part of the people who make PostgreSQL, or that PostgreSQL is a generic term for a general type of product. Thus, unless you want the trademark to become a generic term, you do have an obligation to enforce it or lose it.

(as the other commentator said, this is all completely distinct from copyright: trademark law is to a large degree a consumer protection law, in that it allows consumers to be confident that the products they are buying actually come from the company they are buying from. If the PostgreSQL trademark is lost, it's not a matter of the source code to Postgre becoming public domain, but rather the ability for random people to legally (say) distribute malware under the logo)