How about you not accuse people of deliberately trying to cheat thier opponents with no cause.

I prefer to put them next to the ship. Works great for tokens that get wiped at the end of the turn. Doesn't work as great for target lock tokens. It is rather hilarious sometimes how a player's ship is on the left side of the board (having just moved there from the right), but the target lock on that ship is still back on the right side of the board. Usually works out fine though.

It depends of the traffic of the game, if there are too many ships I prefer to put in the base of the ship, but in the early steps or the final steps that there are a few separate ships it doesn't matter, greettings.

Edit: Why can't you delete your own post?

Anyways, on base, on ship, whatever is what I say.

As long as they put them on the table and not on their ship cards, I don't much care.

Tokens in play should be easily discernible by scanning the battlefield itself. Off-table placement can lead to confusion.