A well-thought out and logical reason for calling this runner safe. The only problem is, I can think of equally well-thought out and logical reasons for calling the runner out!
The point you make is one I considered for not calling the runner out. Had she not been obstructed, the whole "slide at the plate" may not have even happened.
On the flip-side: When a runner is awarded a base (or, in this case protected to one) she is liable to be put out if she passes that base.
An analogy would be a runner on first, 3-2 count on batter and runner attempts a steal. The pitch is ball four, but the runner is sliding at second and the catcher makes a throw.
Of course, if the runner is tagged before reaching second, she is not out. If the runner overslides and passes the bag, she can be tagged out.
A wrench in that argument is that runners can legally overrun home (and first), but not second or third. So it might not be an "apples-to-apples" comparison.
I've also considered that even an awarded base must be run legally. Going past the plate without touching it is not running the bases in the legal manner, and always makes the runner subject to an appeal.