Generally just grass or a thin layer of mulch. Landscape fabric can kill the tree if it's not breathable.

I use cardboard under my mulch. I have many area of landscape fabric, really a pain to maintain. Looks OK for about two years, then trouble. I just keep the area around the trees weeded and a very thin layer of mulch. But nothing against the tree. Just weed it, it hardly gets any weeds and it takes about 5 min. once very couple of months to weed.

The "no mulch within a foot of the trunk" statement is rubbish. You may have found that statement as a justification against mulch volcanoes but that's taking it way too far. You never want the mulch to actually touch the trunk (promotes rot) but it only needs to be a couple of inches away at most. And not too thick in that immediate area.

And I will second or third (fourth?) the vote against using landscape fabric :-) It is not at all effective at restraining weed growth and it can prevent proper water penetration. It also prevents the mulch from contributing to the soil quality as it breaks down.

So thin sprinkle of mulch up to the last couple of inches from the tree? Yes? Just barely enough not to touch the trunk?

Also is mulch considered bad and dangerous only if right up against the tree trunk, or anywhere within root crown?

I didn't weed very well at all before applying fabric, it's that plastic Vigoro fabric from Home Depot. The terrain is extremely rocky, and it's just way too much labor to weed properly. Do you think I still should better remove it? Reviewers says it's not apparently very effective, weeds still grow through it. Does this mean its well breathable and allows enough water in? What do you think?

Take the advice of all who responded and skip the landscape fabric - it doesn't work well to stop weeds and its a PITA in the garden!!

Mulch is never considered bad unless piled up against the trunk or stems = mulch volcanoes. But anywhere else not touching the trunk/stems is fine and is actually a very desirable soil covering.

We do three inches of bark mulch at the arboretum. A shallower well around the trunk and not against the bark. The reason for keeping mulch away from right against the tree is to avoid transmitting diseases and fungus from the decaying bark to the tree. In the soil, there are microorganisms that will break down these diseases, etc. but if the bark has any kind of split or hole, etc. in it, there is a possibility for diseases to get a foothold. Better safe than sorry. But really not that big of a deal. I do the mulch and then just brush away the area around the trunk to just a light layer. Three inches of mulch between trees and around those areas does a good job of keeping down weeds. The big problem is volcanoes of mulch all around the tree with it getting higher the closer you get to the tree. The pattern should be the reverse, start out light and gradually get thicker. You have to keep on top of your mulch beds. If it is getting to be a difficult task, there are some chemicals like Preen or corn gluten that will help keep a lot of weed seeds from sprouting.
Also you can spray a weak solution of glyphosate on the weeds between the trees if you don't get too close. There are special herbicides you can get that are forumulated for just "foliar: applications (on the leaves) and they run less of a risk of affecting other plants you don't want to kill IF (big IF) you don't spray on a windy day.

Thank you guys. Will take the darn fabric out and cover it up with bark per your recommendations.

I don't heap mulch against a tree but place a thinner layer around it and right up to the trunk. I have chronically ignored the advice not to do this for my entire life and it has worked out well with nary a problem. But as everyone here knows, I am not a perpetual mulcher. Everything is plantings of some kind so there is no need to add layers of mulch later. Ever.