Yes, you are correct... the backs of leaves are silver'ish. This year, in particular, there are literally thousands of berries on the shrub. Thank you for your help!

Looks like one of the dastardly shrub honeysuckles (Lonicera spp.) to me, probably winter or fragrant honeysuckle. That one is known as Lonicera fragrantissima. It will have had small creamy white flowers earlier in your season, from which the red fruit are now forming. The new stem growth extensions with purplish color is the give-away ID to me. All the honeysuckles are oppositely arranged in leaf and branching, making them easy to separate from many other native species (except viburnums, buckeyes, and dogwoods, of course). The behavior of "...the shrubby undergrowth is almost entirely this shrub..." fits with how many shrub honeysuckles dominate the understory of woodlands when they get the chance. The term that fits is invasive. If you are interested in reducing or eliminating this effect, then you have to reduce/eliminate the flowering so that you don't have massive new fruit production every year. That means repetitive cutting down of the plants, especially right before or during flowering, or resorting to total removal or pesticide application.

I had considered a deciduous holly, too, suja, but the leaves and the shape of the shrub didn't match up. I'm afraid it is autumn olive. I had also considered this, but the leaves didn't look quite right in the pictures I had looked at. After reading sam_md's post, I looked at some more pictures, and the berries are a perfect match, right down to the little brownish spots on them. I checked while I was out walking today, and the undersides of the leaves are indeed silver. Mystery solved, I guess. Too bad. It's really a very handsome plant. I've always read it was a very invasive, undesirable plant, but I can see why it gained popularity when its planting was encouraged. Unfortunately, this particular shrub is located on private property, so I won't be able to chop it down. At least now I'll recognize it if it shows up on my property. I can add it to my list of things to eradicate, along with oriental bittersweet, mile-a-minute vine, garlic mustard, . . . The list never ends. Thanks to both of you for your help.

Could've been Burning Bush (Euonymus alata). Once the leaves drop, small bright red berries remain. It is considered invasive in some areas, including the Mid-Atlantic area (and pops up on the side of the road): Viburnums are very good berry producing shrubs. The birds especially appreciate the native ones. I had a group of robins feasting on my Viburnum acerifolium berries yesterday.