|Often means the computer you're using is a public one; as in a library, school or similar? Also the internet connection may not be secure - again a public one is typically considered not secure.|
Unless someone is hacking, or you have managed to connect to fake (and thus not secure) internet connection - not your own home one for example - then unless they have installed malware on your computer you '"ought" to be safe.
But more information as to how and where you were connecting to the internet would be useful here; if only to more clearly and accurately answer your concerns.
Incidentally it might even be that the site you were addressing isn't genuine either. Without giving personal information here (login/passwords and home contact details, or account info etc.) what was the site which gave the refusal/response?