Consider solder and soldering process test.
A solder stencil opening well in excess of the pad is created and the solder paste must coalesce into a nice solder bump. You can see it on some electronics mainboards. It's entirely not an error.
I have seen this used as the special pads to which test and programming pins connect, the excess of the stencil opening defines the shape and height of the bump and is thus critical.
Also not an error.
Eagle should be able to differentiate between design rules that are there because of strict manufacturing limitations (like smallest drill bit is 0.3mm and that's it), but then, there are design rules that are "just nice" or sanity, or increasing reliability.
So, you need Manufacturing rules, Project design rules and individual component design rules.
You can not go "under" manufacturing design rules, but you can, and many times go under your common sense rules at selected places.
My PCB maker has 0.15mm trace 0.15mm gap rule.
But of course, I intend as far as possible to keep at least 0.3mm trace everywhere. This, of course is broken at some places.
This is the real world and that's how it shuold work.
Instead od "DRC..." menu, we should have a new one, that would be design rules, and checking them being only a small part of that.
The personal/project design rules could also incorporate things such as grid preferences, because some projects do use some weird grid settings.