The correct position is that the pebbles can be collected anywhere within the boundaries of al-Haram (the territory of Makkah ).
It is known that the Prophet (peace be on him) did not ask that the pebbles for Jamratul Aqabah be picked up for him from Muzdalifa. They were picked up for him, in the Morning, after leaving Muzdalifa and on entering Mina. The rest of the pebbles were picked up for him, from Mina too.
Some pilgrims wash the pebbles, but this is not recommended.