Q.Bert
Seeing Paul was talking to Christians. Then it is obvious that he was saying that all of US that accepted Christ are anointed. Because Christ is alive and therefore can still anoint His followers.
Of course you probably think of "anointed" as something being poured out on you, oil, water, Holy Spirit.
Another definition of "anointed" is: "To choose by, or as if by divine intervention." {American Heritage Dictionary)
"You did not choose me, but I chose you and appointed you to go and bear fruit—fruit that will last. ..." John 15:16
"But you are a chosen people, a royal priesthood, a holy nation, a people belonging to God, that you may declare the praises of him who called you out of darkness into his wonderful light." 1 Pet 2:9
David was "anointed" as a young boy showing he was chosen to be the next King, even though it was years later before he became King.