After an hour or two playing around with this problem, I decided I'd had enough and went out to lunch. I was at a place with no WiFi service...I got a call. When it ended, I tried clicking on WebView update. NOthing. Then I tried Chrome and...voila! It connected. And it updated (tho slowly, as the mobile service was incredibly slow). When it finished, I tried WebView again, and it worked. So now they are both updated. I could swear that I tried it at home without WiFi turned on, but maybe I didn't. Anyway, I don't know if that's the solution or not, but you might want to try it updating through your carrier instead of WiFi. I doubt that Google will ever be a source to determine just what the problem really is.