(1) According to some interpretations of Jewish law, embalming is forbidden. There is some debate among Jewish sages as to the precise point where cleansing the body ends and embalming begins.
(2) According to Jewish law, shiva begins as soon as the body is buried.
Placing someone in their tomb is presumably a burial.
I'm not saying DonQ is necessarily right - just that his viewpoint merits consideration and is not automatically "baloney".
Perhaps Joseph of Arimathea, being a Pharisee, felt that washing Jesus and wrapping him in a shroud fulfilled the mitzvah. Perhaps some other friends of Jesus, who did not come from a Pharisaic background, had a different opinion about whether the body had been properly embalmed or buried.
Further, most Christians take for granted that Christ's being placed in the tomb constituted a burial, as the early creeds attest.
All other things being equal, I don't think there's any principle of Jewish law which says that a body cannot be considered buried until it is washed in spices and ointments. I believe simply washing the body in accordance with ritual ablutions would suffice.