This is one thing I don't understand. Anybody knows why?
Any transfer at a bet table, be it the white ball flipped out of the wheel onto the floor, money, chips, bonus swipe cards, free bet credit slips or any other items requires SEPERATION from the player to the dealer or any other pit staff. This mostly eliminates any dishonest activity.
The standard way they do this is to place your money, chips etc. on the table and then the dealer handles it as is normal. On wins the dealer always puts your chips on the table and slides them to you.
You should also notice that the dealer displays both sides of his/her hands to show that no trickery has taken place. Keep in mind all play is monitored by a number of cameras so any suspicious activity can be reviewed in detail. The most common use for these cameras is to resolve bet placement of same value cash chips or chips wrongly or fraudulently placed.
Casinos/gaming authorities/police require fair play, so all the procedures relate to this. Cheating eats into casino profits, they go to great lengths to minimise it.