In you scenario here, David, the cupholders are some CSS changes you have made. The core files are the engine that runs your site. We will issue support, all we ask is that thoe modified files you are running are reverted to be stock while we look at the issue.
I would note, this is the same for themes, plugins, applications etc. We always ask for things to be tested without those modifications. We're certainly not saying we will not give support. We are simply asking you to ensure we can issue that support in the correct manner.