Well, not being able to distinguish between IP addresses and domains, but demanding unrestricted access to WHOIS database contents. Great strategy. It's highly foolish: I can't, for the life of me, imagine a situation where the domain owner is really the interesting piece of information. On the contrary, it's almost always about IP addresses - and these are assigned to the registries and then to the providers, but these assignments are public. The assignments after that - i.e., how the providers allocate the addresses further - are not in any public-access WHOIS databases, but are stored with the providers. Let's think through a few cases:
Illegal upload or download of protected works: To clarify such cases, you need the user's IP address and the assignment over time - because these are often dynamic addresses. The information can only be provided by the dial-up provider in whose area the IP is located. This assignment to the provider is publicly queryable via WHOIS, but everything else can only be obtained from the provider.
Illegally operated server: The domain under which it runs is initially irrelevant - more interesting is the IP of the host on which the stuff is located. True, the domain may provide clues about co-responsible parties, but the interesting part is the IP - because you can get the hoster for the system through it, and they have records of who they provided this server to. Moreover, only the hoster can have access logs for this server, through which, for example, it could be determined which IP made the upload - and then we're back to the first case.
Email with insults, threats, or other prohibited content: Here, the domain probably helps very little - more interesting is the IP of the servers on which the emails were packaged and delivered. Because through access logs, you can get the IP of the delivering or retrieving system and then, with the first point, get back to the user.
Sorry, but I really don't see any reason why domain data should be public or why law enforcement agencies need urgent access to the data - sure, trademark lawyers would like that, but I don't think this is about facilitating access for trademark lawyers...
To me, the whole thing sounds like another case of demands being made without a real concrete need. Just as surveillance measures without good reason are repeatedly made public - and then the investigative authorities are once again in the line of fire. It would be nice if, with all these demands from the authorities, there were concrete reasons why this demand is being made, so that one could think about real solutions to their problems - after all, the refusal to provide data is not about hindering the investigative authorities, but about ensuring data protection.