To the phantom thumb downers... a "right of way" is a legal term meaning [from Black's] "The right of passage or of way is a servitude imposed by law or by convention, and by virtue of which one has a right to pass on foot, or horseback, or in a vehicle, to drive beasts of burden or carts, through the estate of another." and "'Right of way', in its strict meaning, is the right of passage over another’s ground; and in its legal and generally accepted meaning, in reference to a railway, it is a mere easement in the lands of others, obtained by lawful condemnation to public use or by purchase."
That is to say that for a public road, vehicles and pedestrians both have rights of way.
The term you are thinking of is "priority", which applies only at junctions. If pedestrians simply had priority by virtue of putting their foot on the road, then we wouldn't need zebra crossings, would we?