I'm sure it was mentioned somewhere that it was established that she left the hotel for that day, not simply went to another room within it. You may be right, though.
I'm not saying anything as a certain fact. I'm applying Occam's Razor; the principle that the simplest answer, the one requiring the fewest assumptions, is usually the correct one. All of the others seem to involve multiple more steps and assumptions.
The placement of her hands may be unusual. However, it is a perfectly plausible method and is easy to do. Firearms are actually often notoriously difficult to lift fingerprints from. Example, we know for a certain fact that her hand was on it. Therefore it follows that there should be fingerprints even if it was placed in her hands after she was dead? There were none, though.