Do you know what this is?

Three or four years ago, I noticed a new plant growing on the north side of our row of lilac bushes (probably "planted" there by a bird as it... well... you know). At first I thought it was wild raspberries, and I was delighted. But it didn't turn out to be that, and I've continued to wonder what it is. This year as I mowed past it one time, I noticed that it was very full of blossoms... little insignificant-looking white blossoms, hanging down.

It suddenly dawned on me a few days ago that I should take pictures of it and try to figure out what it is. Thanks to all the rains, the mosquitoes are terribly thick this year, and the north side of the lilacs is one of their favorite spots, so I went out in full sun, thinking they wouldn't be so bad. Wrong. They were awful! It was like a Deep Woods Off commercial! I had to take pics really fast or get eaten alive, so the photos aren't the best. But here's what the bush looks like now. Maybe someone can help me identify it (Grace?).

A cropped close-up of the leaves:

And the berries as they look now:

I did lots of Googling. Finally, in the process of writing this post and searching some more, the closest I could come was a wild black currant, as shown here. Whaddya think? Is that it? Anybody else have bushes like this?