Depending on the porosity, etc, of the material this aging can be merely on the surface or extend down through the stone towards its center. Sometimes this occurs on only one side if the piece hasn't been disturbed and one side remained more protected than the other. Soils can also polish the surfaces. Older tools sometimes have recent chipping or reworking on them which is obvious because it lacks the characteristic patina found on h rst of the piece.
Even very ancient rock has moisture in it that remains in it so long as the cortex is undisturbed. The flintknapper may begin working on material that looks very dark, only to see it change later as it dries out, to something quite light in color. This factor doesn't help much since most fakes would dry out quickly anyway.
Some newer relics - particularly those used for small arrowheads- were sometimes heat-treated, a process which can dramatically alter the characteristics. Typically it makes material like chert much more colorful. It also makes the inside glassier and easier to work, and when worked, it's sharper. The disadvantage is that it makes material more brittle, too brittle for axes.
It's true that sometimes it's not easy to tell a real from a fake- there have been cases where knowledgable people were fooled by very talented fakers using assorted recipes and methods. Most fakers aren't that good though- they leave the smell of Old Mill furniture polish on the item, or creosote, use gemstone tumblers and polishes, etc- but they are not making their work to be donated to some museum but rather to fool the collector so they can get some cash. But often traces of their fakery end up under flaws in the material and can be detected. One of my friends spots traces of coffee, manure, etc all the time in otherwise good modern replicas taken to him for identification.