It doesn't directly influence price.
However: a off-exchange deal influences the market indirectly: maybe the seller would've sold on market instead, so the supply is withheld. Maybe the seller re-buys coins on the market because he now has less coins. Same for the buyer.
It's most clear with a miner who has to sell to cover fiat cost: hadn't he managed to sell off-exchange, he would sell on on-exchange.
Maybe it's not so clear-cut with early adopters: maybe they wouldn't have sold had they not been contacted with a good offer to sell a sizable chunk, maybe even invisibly to the tax man.
So I think the truth lies somewhere in the middle: off-exchange trades do influence the price on the exchanges indirectly, but probably not to the full extent.