You can't play solo as in having the world to yourself. You can play solo as in playing alone within a world/server filled with other players who will not be playing alone. There are no private or local servers.
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I'm 100% sure. I watched the conference as well. There will be private servers that you'll be able to play alone on but they're not going to be adding those until later on. As of right now, at launch you will not be able to play on a server by yourself. You will HAVE to play with other people on the same server as you. But whether or not you associate with them is up to you.
Tried getting interested in Bethesda RPGs but I never seem to get invested in them. I know a new Fallout game is a big deal but I'm more hyped for Doom Eternal