I know that scene safety is drilled into our heads since day one of EMT school. I will somewhat part company with folks here.
When I was in the ghetto, if we waited for the police on every OD or call with the potential for violence, we would have rarely gotten out of the rig.
Bottom line- you need to know your area, you need to know your capabilities, and maintain a situational awareness of your surroundings. If you are pulling up to a scene and notice dozens of angry people running around, then yes, it makes sense to wait until the scene is secure. It depends on how much prearrival information you receive, your knowledge of the area, and what the call is dispatched as. Maybe you are familiar with the address and know it's a drug house or gang hangout- then yes, wait for back up. Maybe you know a certain area is "hot"- meaning gang warfare is going on. Wait for back up. This is when experience comes in handy.
If you decide to wait before making patient contact, you damn well had better be able to JUSTIFY your rationale because a lawyer will certainly want some proof later: active shooting, threatening bystanders, warnings from dispatch that the scene is not safe, etc. Simply saying that you did not feel safe is not good enough. In some areas, the whole neighborhood is "unsafe" by the standard definition of the word, but if that's your area, that's part of the deal. Prehospital care is by definition unpredictable, and that is exactly why most of us got into this business. If you want somewhat safe, secure, serene surroundings, a hospital is probably where you need to be.
I'm no cowboy, I am never reckless, nor would I knowingly put myself or my partner in danger. I simply think folks sometimes overstate the dangers we face. The vast majority of times when I felt my safety in jeopardy was in cases that had nothing to do with a violent injury like a GSW or beating- they were from medical or cardiac calls when bystanders and/or family started acting up, or when a domestic dispute broke out while we were on scene.
In my experience, in 99% of our calls, even the goofiest, most angry, violent folks do not direct their anger or ire towards us. As long as you make it clear you are there to do the job someone called you to do, generally they leave you alone. Remember- someone called YOU for help, and you are supposed to be the professional that is there to mitigate a problem.