But that depends on what kind of "individual transactions" we mean.

Trades are symmetrical. A buy only goes through if it matches with somebody else's sell on the other side. And when you're "buying" one currency with another currency that also looks similar to "selling" the second currency for the first one. There is no one "price" of a coin on the market, each transaction has a "price" that the two parties agree to. We often treat the most recent trade or some average of recent trades as "the" price but that is an abstraction, not reality. The reality is that each individual market participant has their own preferences around whether they want to acquire or trade away particular coins. There's no centralized bucket that all sells go through or all buys go through that push a quantity called "price" around. Sometimes you can think that way as a rule of thumb, but it's not the way the actual market operates.

The global supply is affected

The question is not "is global supply affected", that's backwards. You are trying to argue that global supply affects something else: the buying and selling decisions of market participants.

but at the end of the day it is the price that the market dictates

The price is what buyers and sellers agree to. There is no separate entity called "the market" that dictates what "the price" is, that's a simplified abstraction of aggregating lots of individual decisions.

At least that's the theory

Yes, a theory that's probably wrong.