Is it then supposed to be a simple coincidence that the only time I used the email address was to register for a site based in the DR and now I'm getting unsolicited email to it from another DR business?
How about this:
You register on a DR website with a unique email address that you will only use for that website. Over time, this DR website sends you email messages, announcing stuff that you might be interested in knowing, either because you asked the site to do this or because it is a default setting.
The website has no control over what route these emails take to get to you. One time an email may be routed through Russia, another time an email may go through Canada, Smuckmagosh Ohio and then through San Francisco before landing in your inbox.
Each hop and there are often a few, may record your email address. Most relays don't care and never look at these logs if they are created at all. But some admins do, why? Only they can say? So even if you haven't sent an email using this unique address, if you have received even just one, that address is out there somewhere.
For me, I can get about 8 months use out of an address before, the signal to noise ratio causes me to change it. I use unique aliases for most websites. My primary alias which everything gets routed to, is eventually discovered by those who make their living doing this type of thing.
It seems all sorts of companies will pay for a list of verified email addresses. Where there is a market for something...