I don't think that's fair, since they are not really remakes, just movies based on the same source material. That's like saying that the two Prefontaine movies were remakes of each other, or that Hamlet (Gibson) and Hamlet (Branaugh) are remakes. Or maybe you could enter each into the fray, as both Red Dragon and Manhunter were based on the same source material. Oh, now I'm confused....
Yeah, it's a toughie. I'm inclined to count a movie based on the same source material. The newer one is a remake even if it isn't directly inspired by the first movie. (Otherwise I think we have to throw out too many movies that everybody would call remakes.)
Along those lines, consider the Kevin Costner and Patrick Bergin Robin Hood movies. I agree that neither one is actually based on the other, but they are both remakes of the same older movies. And according to IMDB they were released 31 days apart. Beat that.
I don't think that's an unreasonable point of view, but I don't think it's necessarily so.
For example, imagine that someone decides tomorrow to make a movie out of his favorite novel, "No Blade of Grass" by John Christopher. Filming is completed, and he doesn't learn until after his movie is released that it was already made into a pretty lousy movie 35 years ago. Would it not still be a remake? Critics and anyone else who saw the first movie would certainly call it a remake. Would they be wrong?
Yes, I (at least) would consider anyone calling that a remake wrong. If the first adaptation had no influence over the second, you can say that they had a common ancestor, but that's all.
And by that logic, I don't think Red Dragon should be considered a remake of Manhunter. Even though some of the same important creative people may have been involved (like cinematographer Dante Spinotti), Red Dragon was clearly intended as the third film in the Anthony Hopkins Silence of the Lambs and Hannibal series, rather than as a re-interpretation of the previous version. The original may have had some peripheral, tangential influence on the remake second version, but the second one would have been made much like it was regardless. However, the fact remains that the novel "Red Dragon" was made into a movie in 1986, and then it was re-made in 2002. I think that the intent and knowledge of the filmmaker is beside the point in a case like this. Red Dragon is a remake of Manhunter.
Honestly, though, I wouldn't really call Valmont a remake of Dangerous Liaisons either. I just think that a reasonable argument can be made. I don't think there are hard and fast rules here.
How about Rio Bravo (1959) and El Dorado (1966). I don't know if you'd consider them remakes in the strictest sense of the word, but they're both pretty similar.
Three versions of Dune, 1973, 1984, and 2000. Though I'm not sure if the last one counted as a real movie release, as imdb lists it as a "3 part mini-series".