@John712, thanks for the AV comparatives PDF. I've read AV comparatives articles for many years, but I didn't look at the privacy one. Looks like all of the major brands transmit non-malicious URLs visited.
@mchain, thanks but I already have both of those turned off, it's 1 of the first things I do when installing Avast.
@DavidR, like I said in the original post, I did a custom install and I only have web and behavior shields installed (and also file shield...I didn't mention that). I've tripple-checked by doing a temporary "Modify" of the Avast program using Control Panel, and only those 3 items are checked. Also, there's nothing listed in the Control Panel programs list that shouldn't be there.
Only Avast's developers know for sure, but since I rarely get popup messages from Avast, and now I get one only seconds after doing Internet searches about drivers, and the message is about "software problems", I'd have to bet that Avast is monitoring the searches.