Yes. There is nothing magical here. If two people look at the same object from two different viewpoints, then the background they see behind the object will be different. When I'm sitting at my dining table, I might see a salt-shaker in front of my wife. My wife will see the salt shaker in front of me. My daughter will see the salt shaker too, but from her point of view it might be in front of my son. All these points of view are valid.
When we are talking about the position of planets in the night sky, it is convenient to describe them relative to the background of the stars, as we see them from Earth. It would not be convenient to describe them relative to the background seen from Mars or from the centre of the solar system, because there is nobody there. It's not that those viewpoints are invalid, they just aren't much use to someone on Earth.
Although we might say "Mars is in Aries", this is just a figure of speech, which means "From Earth, the position of Mars is such that it is in front of the region of the sky that we call Aries." It doesn't mean there is any particular physical connection between those stars and the planet at that time or any other time.
It isn't more accurate, nor more correct to describe the background stars of a planet from a point of view close to the sun. This isn't a "problem".