We can see things moving faster than light

Something subtle isn't right.  If an entity outside the Hubble sphere emits a photon directly at us, that photon must already be moving away from us at a speed greater than the speed of light, from our reference frame.  Because that's the definition of what the Hubble sphere IS.  "The spherical area surrounding our reference frame, outside of which, all objects are moving away from our reference frame at a speed greater than that of light."
I say that object MUST be moving away at greater than light speed because by definition OF the Hubble sphere, EVERYTHING outside that horizon MUST be moving away at greater than light speed.  
And since the universe is expanding, (and anything outside the Hubble sphere is moving faster than the speed of light AWAY from us, in it's local reference frame), 
that photon would already be fighting a no-win battle.  It would have to be moving directly towards our reference frame at GREATER than the speed of light, in it's local reference frame, simply to counteract the speed of the expansion of space JUST outside the Hubble sphere.  
It would violate special relativity by 'swimming upstream' fast enough to get INSIDE the Hubble sphere from the OUTSIDE.
You may be able to show me the math, but I won't get it, I'm no mathematician.  But you don't NEED math to argue what is actually a logic problem.  Using the definitions of both the entities AND the concepts that were described in this video, I don't care what the math says, you'd be introducing a logical paradox.
That's my story and I'm sticking with it.  Sorry if it's not the most elegant composition of words, sentences, and paragraphs, I basically wrote it from start to finish in one go, (so I wouldn't lose the idea I was trying to 'argue' by constantly going back and forth editing).

Also, I could easily be wrong, 
but I think my logic is correct, and that's why I started by writing 
"Something subtle isn't right."  
It may be a subtle misunderstanding on my part...

Pretty Strange Down The Rabbit Hole.