Is it possible for a living being to fossilize into a mineral valuable enough that there could be conflict as to whether its material value is higher than its scientific value?
Possibly, yes, but in all practicality, no. In general, veins of concentrated ore occur in igneous rock, the result of a magma rich in the valiable element being extruded at that point. (Note that substnatially more such deposits are extruded underground than on the surface.)
A fossil is, by definition, a relic of a living thing preserved in the rock. Aside from unaltered material (extremely rare) and imprint/hollow remains (there’s a film where the leaf used to rest; there’s a shell-shaped hole where the shell used to be), nearly all fossils result from petrifaction – the replacement of decayable organic material by (usually suspended) mineral matter in a way that preserves the characteristics of the original.
That mineral matter may be rich in something. There are a very few fossils composed of more-or-less semi-precious stones. But it’s excessively rare that the replacement material is anything with intrinsic worth on its own to begin with. For it to be something on the order of gold, platinum, etc., would be sufficiently unlikely as to warrant a “no” answer even though it’s technically possible.
It’s technically possible that sometime before January 20, 2009, a meteorite will survive its flaming descent through the atmosphere and end up on the White House lawn – and it’s technically possible that the vagaries of its descent and what happens to it during it will result in it being a recognizable bust of George W. Bush as it lands.
But don’t take any bets on its happening. And finding a gold dinosaur fossil, or even a nickel trilobite, is going to be on about the sam order of improbability, IMO.
You can find opalized fossils, and opals are precious to semiprecious stones.
In addition to opal, you get many pyritized fossils that are, IMO, more valuable for their prettiness than their scientific value. I have some ammonites like that. But that’s only Fool’s Gold.
Then there is the T. Rex skull with gold fillings…
I could’ve sworn I read, as a kid, that one of the few T. Rex skeletons found up until that time was of iron, but a quick new search and perusal of the Wikipedia article on T. Rex skeletons fails to confirm this.
Darn it, I recently saw a news article about fossils containing lots of iron in them - so much so that the bones were dull red. Can’t find a link right now, however. 
I’ve got some pyrite ammonoids. Nice and pretty and shiny.
eta-or what MrDibble said.
Related but maybe off topic: If I wanted to fossilize myself in gold (money is no object since I’m immensly wealthy), how would I do it?
To what extent do you want it to still be you? You don’t contain a lot of gold at the moment - so if your ‘fossil’ is to have a fairly high gold content, it’s really going to just be a casting made in a mould formed around your body. You can do that today, without going to all the trouble of dying.
Would you count organisms preserved in amber? This one has a frog in it.
Amber isn’t quite described by the OP, but it generally fits the science v. bauble conundrum.
ETA: Sorry Aioua, I didn’t see your post before replying.
Some of those fossilized opals can be quite pricey .
21.7 grams for AUD$2,563.50. Gold is about AUD$ 28.50/gram.
Thanks for all the replies. It seems that the opal and the pyritized fossils are valuable because they are fossils. Not because of the material itself. This means that they would still be kept in the fossil form, thus still being somewhat available for scientific study. ETA: Ditto for the amber pieces.
I was thinking more along the lines of a material that you would want to just cut up, shape and polish into jewelry, for example, or a rare needed component for an industrial reaction, or something else that would mean the destruction of the fossil.
If you had an ammonite made of diamond, wouldn’t it be far more valuable in its natural form than cut into an ordinary diamond shape? Such a thing would be literally one of a kind.
I haven’t been able to find a specific cite, but I would imagine that only water-soluable minerals are likely to be able to form fossils. So no fossils made of diamond or sapphire for instance. Too bad; a tyrannosaurus skull called “The Jade Dragon” would be a great MacGuffin for a movie or novel.
Good point. I think we might be reaching the limits of this question.
Now, on the impossible assumption of a diamond ammonite, would it look pretty at all? How much would you have to polish it and alter it before it looks like a jewel? Would it still be a fossil, or a diamond shaped as a fossil?
Then again, there is the issue of what would be the real scientific value of one more ammonite. Probably next to zero.
I don’t know anything about fossilization, but I am going to agree with Lumpy here. I don’t know about saphire, but certainly the conditions required to form diamond would destroy any recognizable remnant of a fossil.
Precious minerals aren’t things that just precipitate out of solution. They require a specific set of conditions that are unlikely to occure, or else they wouldn’t be precious.
Gold can precipitate out of solution, just not ordinary water. But you certainly get it precipitating around black smokers with superheated fluids.