The first part of the argumentation is basically right: external objects influence the gravitational field so that the event horizon of the black hole in the middle will no longer be "exactly spherical and isotropic" when additional objects' gravity distorts the field.
Well, the reality is that even the spacetime refuses to be spherically symmetric in the presence of objects around the black hole that break the spherical symmetry. The spacetime itself is curved, not spherically symmetric, so we couldn't even define what it would mean for the event horizon to "remain" spherically symmetric.
However, the second part of the argumentation isn't right. These additional objects can't retroactively redefine the event horizon and "pull" some points from the black hole interior.
The reason is that the black hole interior – whose boundary is, by definition, the event horizon – has a clear and totally unambiguous definition. The point $P$ in spacetime is said to be in the black hole interior if there exists no future-directed time-like trajectory starting at $P$ that ends in the asymptotic Minkowski region at infinity, the "scri plus". (In plain English: if no massive particle has any chance to escape from this point to the safe exterior.)
With additional objects distorting the gravitational field, we are effectively given a new spacetime (including its future shape) and we have to solve the exercise of dividing the spacetime into the black hole interior and the black hole exterior again – the results from a different spacetime, one without the stars and the extra curvature they caused, is not useful anymore.
When we run the exercise again, from scratch, we will have a clear separation of the spacetime into the interior and the exterior again, and the boundary in between these two parts is the event horizon. There can't be any sense in which one spacetime point was "previously" inside but it is outside "later" when the star is added.
Again, the separation only makes sense for spacetime points, not for "points of 3D space". The spacetime points are defined by their location as well as the timing – there is no "before" and "after" for them. And for the spacetime points, there exists an unambiguous procedure or definition that decides whether the spacetime point is inside or outside. This procedure or definition depends on the shape of the whole spacetime (including and especially in the future). But the shape of the whole spacetime must be considered to be well-defined and fixed for the notion to be well-defined. One can't talk about "two different spacetime shapes" at the same moment.
In other words, one might say that an oscillating star in the vicinity of the black hole will make the event horizon oscillate as well. But there will still exist a hypersurface given by an equation $f(x,y,z,t)=0$ – where the function $f$ may depend on $t$ and not just on $x,y,z$ – which will define the event horizon, the boundary between the interior and the exterior. From points in the interior, one can't get out; from those in the exterior, one is out and can stay there.