Any property, regardless of who owns it, may not be legally broken into. Any "agent", which I mean in a legal sense like a superintendent, property manager, security guard, etc., has authority to deny entry or remove someone for any reason. This legal authority dates back at least a thousand years in common law and is unquestionable.Ummm, it was a private installation and they were security with legal authority to protect it.
Whoa now, not sure where you're getting any sort of legal authority from? There was nothing legal going on there. It was specifically stated to be not Shield. Whoever those two guards answered to, it wasn't any sort of legal government authority.
It seemed to be a facility designed specifically for medical experiments that were NOT legal, be it whatever questionable procedures were used on Coulson, or experimenting on still-alive (?) aliens. This was the definition of off the books and beyond the law.
If you come to a property, the door is locked, the person inside refuses you entry, and you break in, then the person inside, whether they are the owner or the owner's agent, has authority to remove you. If you are pointing a gun at them, you are already a criminal and they have legal right to defend themselves. This isn't even anything radical like "Stand your ground"; it is the law in every jurisdiction I can think of.
As far as "off the books" giving you any legal or moral defence, I suggest you try breaking into a CIA base because you are hungry and want to raid the fridge and see how far that gets you.
Yes, Skye was dying. People die; we all will. It would be ironic if Coulson goes through all of that, and Skye ends up slipping in the shower and cracking her head next episode. Her medical condition did not justify killing two people and destroying research that, down the road, could have benefitted billions of people.