No, I think what's happening is someone else is confused what their email address is. With Gmail, dots are not significant; any email address with dots is equivalent to the email address without any dots. (So you may have signed up as first.last@, but your email address under the hood is really firstlast. You can also send mail to your [email protected], and it will be delivered to you.)

I expect that someone else with the same name as you occasionally (or all the time) forgets that their actual email address is [email protected] or [email protected] or some other similar combo, and enters your email into signup forms. Or has friends who guessed their email address and got it wrong. Or something.

That other person doesn't have access to your information.