No, Remington 700's are no more accurate than Howa 1500, Savage 10/110, Sako TRG, Tikka, or Win70s.
The Win70 action is the basis for the FN SPR series of tactical rifles, and they shoot like a house on fire.
Heck, Zastava is still making a tactical rifle based on the m98 action (which still has a faster lock time than an AR-15).
So no, accuracy is not a product of a particular brand of action.
Jimro