Actually, whether deliberate or not, I'd say the assistant should find another line of work. This is a pretty major mistake that would get you fired in a wide range of jobs that involve managing emails.
This kind of thing is one reason I never share personal details for screening. It is one thing to trust that the recipient will do what they say and delete your personal information after the visit. It is another thing to assume that they are sufficiently diligent to make sure that your information won't be compromised by mistake, by an inexperienced assistant, or by someone in LE.
Yes, I realize that this was just an email address and you should of course use a hobby email address, which I do. My point is that the same person who makes this mistake could either not know good procedures or not carefully follow them for handling personal information that goes beyond hobby emails and phone numbers.
I have received these types of "cc: instead of bcc:" messages a couple of times, and it is absolutely amazing to me the number of people who use real world email addresses, from work no less, that you can google and get their picture, bio, job title, etc. in 10 seconds flat. Obviously being "outed" is not a concern to them, but a bit foolish for one to conclude that it never will be a concern to them for the rest of time given that everything on the internet is written in pen not pencil.