There no reason why you can't use a little grease in your 870. Grease will usually make a guns action operate a little smoother, and unlike oil, it won't run off, dry out, or evaporate.
In my 870's I applied a little grease on the slide, the front face of the hammer, and the end of the action bar lock lever.
Any where you see wear can use a little grease.
You have that one backward.
The old standard was "If it rotates oil it, if it slides, grease it".
I personally don't hold to that and will use grease on any application.