I'm pretty sure the answer to the question in title is "No". But why?
Below is a naive Newtonian simulation I made. You can see that in the animation, both black hole's horizons seem to "recede" for a moment as the black holes pass each other. The black holes in the animation are NOT MERGING. Therefore any explanation involving merger and subsequent expansion of the new horizon does not cover this situation.
The color of the pixels describes escape velocity at a given point. Black pixels have the value higher than speed of light.
What am I illustrating here is, that if two black holes are too close to each other, their gravity must cancel out. Lagrangian point would appear somewhere in between. Yet we know that nothing should be allowed to escape. At the same time, quantum mechanics requires the surface of the black hole to be directly proportional to it's mass. Which is not the case in the simulation we see.
How does event horizon survive distortion caused by another black hole, when two black holes are extremely close to each other?