The Intel push pins are horrible, its not just you being worried.
However, they usually work well enough even though they always feel cheap and fragile.
I am using the push pins on my computer (begrudgingly) and my processor still rarely ever passes 40c. That isn't on stock paste, but it is with the stock heat sink connected with the push pins the regular way.
I was really worried when I started mine up the first time too, because even when I looked at the back of the motherboard it was clear that the push pins weren't at equal depths and one of them didn't even appear to go in correctly at all.
However, it all functions according to plan that way in my PC and for pretty much everybody else too.
The CPU should shut itself off really quickly if its not on there right.
Generally speaking, you have to do something colossally stupid to blow up a newer CPU. They pretty much all have sensors that will shut the processor completely off if it notices upward spiraling temperatures.
There is a video on the internet where this idiot took a really old processor and didn't even attach the heat sink properly so that he could start gaming and then pull the heat sink off in the middle of the game. When he did it literally blew a hole in the top of the processor after a loud pop.
Even if you were to do something equally stupid today, its not supposed to break, it is supposed to detect it within milliseconds and shut itself down to prevent such eventualities.
Whether it actually does that is up for debate. I haven't personally tested it and I don't intend to test it with my 3570k either. I don't have that kind of money to waste.
I would, however, love to hear from someone with enough money that they don't care about paying another $200 if it does break and who has tried it.
In short, your concerns are valid, but its probably like its supposed to be and if it isn't there probably won't be any damage.
- Edit - A video kinda sorta like what I meant about what not to do.
http://www.youtube.com/watch?v=ssL1DA_K0sI
- Edit 2 - The AMD Duron chip in that video was released in 2000. Chips available in 2012 are, again, not supposed to have this happen.