If you get on reddit at work for work-related reasons, you should be fine - and if you won't be, this isn't going to help with the problems in your office.
No, it just means you enjoy reading it and you're willing to break some rule you probably consider dumb and inconsequential.
Why do you think people have to have a "strong need" to be willing to break workplaces rules?
I've also been the person being asked "hey, just between us, how can I check my email/MySpace/LiveJournal/Facebook/Flavor-of-the-week?" Answer: Get a smartphone, use their app or check your email during breaks on your phone not on the company network. Some places are more rigid about this and some are less. I also tell businesses that I can do some measure of blocking, but that at its core things like this are a business and HR policy thing as much as they're a technical issue to be addressed.
And finally, I've been the person charging for cleaning up viruses, doing nuke-and-paves, and (fortunately only once) restoring from backup after what I'll still call "stupid user tricks" when a senior partner wanted a newer version of Office and went to download it. Ain't Cryptolocker fun?