I can't get your point of contention ! Could you clearly state them again !
What I am saying is: from the outside observer's (like the scientists observing the effects of a blackhole and measuring it's size) an object falling into a blackhole will take infinite amount of time to actually fall into it.
Since the mass of a blackhole is a function of mass of stuff that has fallen into it ( including at the time of it's birth), how since the instance of it's birth till now (from outside observer point of view) in a few billion years it grew to this size when from from an outside observer point of view the stuff never actually fell into the event horizon and thus the singularity.
And yet observationally, it is there, and have grown within a finite amount of (outside obversers) time where as it should not have been.
Did I make any sense :/