well, apparently you can :)
Indeed, and people will understand you. But it is considered grammatically incorrect slang (primarily of American origin) to replace adverbs with adjectives. "That hurt really badly" -> "That hurt real bad". An English teacher would mark you down for using such constructs. That's all I meant.
As for your examples of noun phrases with two nouns, I am in agreement with you - the first noun usually takes on the role of adjectival modifier to the second noun. However, this has no bearing on the adjective/adverb issue, as the rules are not the same. I guarantee you that every time you see an adjective that appears to be used as an adverb, it is either grammatically incorrect slang, as above, or actually refers to a noun, such as in the "David is clever" case.
Now I ask, if adjectives can be used as adverbs in grammatically correct speech, why do we even have separate adverbial forms? In your two nouns examples, as you say, there is no adjectival form of "stone", so you have to use stone. But if, as you say, an adjective is being used as an adverb, why not just use the adverbial form of that adjective instead? Wouldn't that make more sense?
lured by Sajmon
*Starts playing a lyre, singing and dancing* Come! Come with me! Come with me to grammarland, where the grass is green, "you're" is never "your", and verbs are always conjugated correctly!