Am I required to show license and attribution for libraries I don't distribute but use on the web server? Whether to produce the web pages I serve or to access data sources, etc.
To phrase it another way; is it about what I distribute, or what I use to produce the software people are using?
This will depend on the licence.
If the licence is conditioned on an obligation, you need to comply with that obligation in order to benefit from the licence.
The obligation may be to show attribution and a copy of the licence upon redistribution of the libraries.
Or, the obligation may be to show attribution and a copy of the licence within any product resulting from the use of the libraries.
There are also licences with no reciprocal obligations.
It depends on the license. Licenses can cover usage, not just distribution.
One example of a license that covers usage is the license for Adobe products. When you buy a 6 seat license only 6 people may use the product at any one time. Windows servers used to have a number of user license. For example if you buy the 100 user license your website cannot legally serve more than 100 simultaneous sessions. This is obviously silly and caused the market to strongly shift to Linux so they stopped it. Today Windows servers have a number of core license. If you've only paid for a quad-core license the OS will only utilise four of your CPU cores.
While GPL mostly concerns itself with distribution, distribution is not the only thing a license can permit or restrict.
Illegal distribution thus falls under two relevant laws: copyright law and contract law (since a license is a contract). Illegal use falls under contract law - you are considered to have broken your licensing agreement with the manufacturer.
