Not true. You incorrectly assume that when the star collapses there is already an event horizon, somewhere. But it isn't. The event horizon will only form at some particular proper time, and at that time most (but not all) of the stellar mass will be trapped by the horizon and will form a singularity (interestingly all the trapped matter will reach the singularity at the same proper time).
This is all very clearly explained here: http://www.aei.mpg.de/~rezzolla/lnotes/mondragone/collapse.p...
Related physics stack-exchange answer: http://physics.stackexchange.com/a/28837
I don't want to sound rude, but you really need to understand GR. The seminal work on the subject is "The Mathematical Theory of Black Holes" by Subrahmanyan Chandrasekhar, you need to know GR very well to be able to understand it, but the pdf I linked is comparatively much simpler on the GR and the mathematics required.