My assessment of cause and effect that led me to write this post was incorrect, and I've updated it. Turns out that what I thought was default behavior was not that at all.
After a relatively painless process of pointing my LouBenjamin.com domain to SquareSpace, I've hit a nasty patch of turbulence. My email ended up being routed to Squarespace instead of staying with BlueHost, where my DNS records are. That's a problem.
About an hour after I thought I had successfully connected my domain to the newly crafted pages, I noticed that no emails were coming in. A closer inspection showed that Apple Mail was complaining that it couldn't connect to my mail servers. I went to BlueHost, and one of their techs saw that the settings for SquareSpace included a CNAME record that routed the mail to (nonexistent) mail accounts at SquareSpace. A later check of the SquareSpace documentation turned up this tidbit:
To keep using your current email provider, you can still connect a third-party domain to Squarespace without disrupting your email service...
Elsewhere, I read this:
If you’re using a Squarespace domain, you can also keep using a third-party email service by adding your email's MX records to your domain settings. To learn more, visit Opening Advanced DNS settings.
And then, there's the bad news sprinkled in the midst of all that: After editing those records, you have to wait for the changes to propagate all around the world. You can even watch its progress on WhatsMyDNS.net, but the process can take up to 72 hours to complete. My email has been down since about 5pm Friday and the fix probably wasn't put in for at least 12 hours. It's now nearly 1:30 on Monday, and I'm still not getting emails.
All I can do for now, is wait. The tech at BlueHost tells me everything looks right. I haven't heard back from SquareSpace, but that may be because they're trying to reply to Lou@LouBenjamin.com.