The fact that products have prices is an empirical fact; Marx's argument is that this fact is only one premise in his 'proof' (using the term loosely) of the "LTV". According to Marx, a good does not have "intrinsic value" any more than it has "intrinsic price". We still say that price determines what goods sell for (even if that sounds tautological).
It's exactly that products do not have prices that is the problem. The apparent 'price' of a product is an epiphenomenon of a particular market, a side effect of the unequal subjective values of the participants (and it's trivial to observe that these clearing prices are determined at the margin, not on average, which makes aggregate LTV even wronger than the regular kind)
In a well-functioning market all products have clearing prices that are easily measured and compared to one another, but this is a mirage that requires constant arbitrage to maintain. The slightest change in unrelated market conditions turns dirt into ore or crude oil into toxic waste, with no objective change in the material itself, only changes in the subjective needs of the participants.
It's fairly trivial to reason from any given intrinsic value theory to absurdities, this is basically the foundation of marginalism and the last 150-odd years of economics.