They can also just switch to a different desktop (on most operating systems). They could instead set their favorite browser to say it's SEB. That's takes about two clicks for computer geeks who have the user agent switcher already enabled, or six clicks for someone who has never done it before. There are probably six or seven ways to get around it, even without getting into anything sophisticated.
Really, it's all kind of like the latch on a bathroom stall - it tells people what behavior is expected, but in no way is it secure in any sense of the word. Safebrowser is really just a strong suggestion letting students know they aren't supposed to use Google during a quiz. If they decide to break the rules, there are a dozen ways for them to do so, many of them simple. That's an administrative and cultural issue, not a technical issue.
Of course, you might ask yourself - am I testing knowledge that the student will need to have immediately in mind in the real world, and not be able to check a reference? Let me use myself as an example. Myself, I've been programing professionally for 17 years and I have reasonably impressive credentials to say I'm competent. I look up programming syntax and such several times every day. Testing how well a programmer can do when they aren't allowed to use reference material is silly because actual programming work does use reference material constantly. Encouraging the student to use reference material is a much better test of real world competence because in the real world the person who uses reference material most effectively does the job most effectively.
All that to say, in many (most?) cases trying to prevent students from referencing outside sources is a futile attempt to make your test WORSE, to make it NOT represent how the student would need to use the information in the real world.
* As a contra example, fighter pilots should immediately know, off the top of their head, what to do when they've been hit by opposing canon fire. No time to check the manual or cheat sheet when you're being shot at. Even in most other emergencies, though, pilots DO pull out the checklist, so for accurate results ONLY the "gunfire" quiz would not be open book.
Hmm, that gets me thinking. In real world application of knowledge, generally you can't refer to a reference in extremely urgent situations. If you can spare a few seconds, you can whip out your smart phone and check. So perhaps use that fact with quizzes - if you expect the students to be able to answer in a split second, set a really tight time limit. If you don't mind if it takes them 30 seconds to answer, perhaps there's no reason they can't use that 30 seconds to check reference material.