I like my binding full, too. I cut the strips 2-1/2 inches and fold in half. Then I align the edge of the binding to the edge of my quilt and use the regular sewing foot...not the 1/4" foot.

Using the regular sewing foot makes it the perfect width to fill the binding. It's closer to 3/8" than 1/4" and looks good. When I fold it over to handstitch and finish, it's just perfect.

I always trim my batting/backing an additional 1/8" wider than my quilt toop. This extra gets folded into the binding, which I cut at 2-1/4", sew onto front, and hand stitch onto back - in the normal method.
This process does 2 things for me, makes a neat, narrow binding and makes a nicely filled binding.

so, i really don't understand i guess; when i trim/square up a quilted quilt i always cut it even...top, batting, backing. then to make binding, bias or straight. i use either 2" or 2 1/2" strips, fold in half lengthwise wrong sides together; press. line up raw edges on the front of the quilt with raw edges of folded binding. stitch 1/4" when i pull the folded edge over to the back for hand stitching the binding is always 'full'; it has the 'sandwich' inside it.
i do always ask a quilt owner if they want me to trim it for them when i finish quilting it, but never thought about someone saying yes, but not wanting it trimmed even.....now i have to think about this; and a question...
if you do not trim it even after quilting how do you trim it?

I would cut a strip of batting and sew it onto the quilt with the binding then turn both to the back making sure I tucked the batting inside the binding as I stitch the binding down. As a longarm quilter I usually trim the backing and the batting 1 inch from the edge of the top. I just think (and my customers like it) that it makes it easier to stitch the binding on. It also leaves plenty of batting to fill the binding. If the quilt is entered into a quilt show Judges will look to see if the binding is "filled". (At least in this area, it's important that the binding be full.)

It surprises me that your longarm quilter trimmed your quilt.
I always sew on my binding before trimming. Next time it may be a good idea to ask her not to trim your quilts.
My binding does have the quilt front, batting and backing in it.
Hope the binding works out for you which ever way you go.

I quilt out to the edge of the quilt but when finished, I lay it out and square up the corners and trim off about an inch all around so I have batting to the edge of the cut quilt then I start to sew on the binding. I like a narrow tight binding as it doesn't take away from the quilt and is very strong.

Me too--batting isn't really necessary in the binding.

This is why I make narrow binding. I trim everything even with the top. I cut my strips 2 inches wide, fold in half sew raw edges to edge of quilt using a .25 inch seam. Then when I fold over to the back and hand stitch it down I don't have ANY "flat" bidning (the binding that exceeds out past the seam allowance without anything to "fill" it) left. I taught myself to quilt, including doing binding and this is how I always did it! lol Maybe I have been doing it wrong all this time, who knows.

I have seen all kinds of ways of doing bindings.
I started off bringing the back fabric over to the front for the binding.
Then I read that although I don't make quilts for shows, they do have some guidelines by way of some kind of standardization; so since I had no one in person to learn from, I thought that this might be some quidance I could use.
I have read that judges like to see firmly filled bindings, so I make mine pretty full with no slack areas.
And I handstitch the back side of the binding to just meet at the line of machine stitching where I attached the binding on the front, with ladder stitch.
Seems to be a workable method for me, and I like the look that it yeileds.

I have always trimed quilts right to the edge of the quilt. When the binding is sewn onto the front at a quarter inch it is then folded to the back for hand stitching and there is always a full binding. I also like to knife edge quilts and also turn the backing to the front and not make any binding at all. All these methods give a nice edge.