Parallax does not depend on the speed of light. The only way light could 'bend' (except by relatistivistic effects), in such a way as would interfere with parallax, is if there were an object made of a perfectly clear substance, of refractive index greater than one, between us and the star or planet. Where is that object? Where is your evidence for it? That object would have to have no spectroscopic absorbtion anywhere between the microwave region and the gamma-ray region, since we do astronomy over that range of frequencies and we haven't seen it. And since refraction is related by the Kramers Kronig relations to absorbtion, that is impossible. You can't bend light unless you absorb it somewhere else in the spectrum.
This is all elementary physics, BTW.
Not true. Light bends as it passes through water to greter than a one degree shift. This is just one such substance that can cause an apparent shift. Your assumption at the baseline is that there is nothing obstructing. Therefore, if you are going to state a distance as fact, you must first prove it a fact rather than assuming it is. This would involve proving absence of interferance or shift. And parallax does not adjust for this. And yes it is elementary physics. So is refraction through water. You are thinking in two dimensions on a best case scenario - as though, forgive the pun, things happen in a vacuum. I'm thinking three dimensionally knowing they do not. There could be a billion obstructions and factors between us and the closest star and you are arguing about the presence of even one.
You can't bounce a laser off a star, so you litterally are guessing it's distance based on a perfect world model with no natural interferance. I'm not stupid, sir, If I hold an amber lense in front of my eye, the entire spectrum shifts. If I look at light through water, the direction from which the light seems to come is not the direction from which it originates. That is the difference between position and percieved position - color and percieved color. I introduce two - just two obstructions and you're off course by light years.
Facts are truisms. If you want to engrave something as a fact, you have to prove it is true. Demonstrating logical plausability given a vacuum and no interferance is worthless if I can insert reasonable doubt. Knowledge is not so useless as not to matter when it's wrong. That has been aptly demonstrated here already. The spotted owl was a great modern example of idiots pontificating about something they knew little about; but, by god they were sure that the poor beast was endangered - to the damaging of many people affected by the statement of "fact." How many people do you suppose die if we send a ship to Alpha Centauri and you don't know if the star is where it "appears" to be or has the frequency of light that it "appears" to have. How bout we strap you into a rocket and aim you at the light and light the butt end of it. How sure are you then. It's different when we know the ship can comfortably get there and back. But when that is not the case, it becomes foolhardy. A fact is something you CAN comfortably bet your life on with no worry. Distance to the nearest star as proposed here by you is not something I'd even consider betting my life on.
10. Errors When we are wrong about a factual matter or in our conduct, we will acknowledge it. We will encourage others to do the same; and thus we will not acquiesce in improper conduct by those whose views we generally support.
Time for full ignore.