You rhetorical question is... whether you should trust a company that already has both your full name, and a list of companies you've worked for (because you gave them both of those things to enable them to publicly display them to people searching for you)... with the information of what your corporate email address is?

They already know your corporate email address. They — and anyone else who sees the public profile they display for you(!) — has all the information required to deduce it. (And privately, they have all the info required to not even have to brute-force it — i.e. they already know some of your coworkers' corporate email addresses, and so the format of the username-part of yours.)

The only thing they don't know, is whether you — the person who claims to have worked for company X, but might not actually — can access that email address.

Is there something scary about them having that information, over-and-above what's scary about them being able to do what they can do with the information you explicitly did choose to give them?

I don't want them emailing me job offers at work, and I also don't want them emailing me "you haven't responded to the job offer we sent to your other address" either, and I have zero faith that won't happen.