I have read that it would slide off the table, because apparently in the frame of the table it experiences a centrifugal force outwards, but I can't seem to agree with that logic.

In the ground frame of reference there is no force in the direction of the groove (let me call it the instantaneous x axis). Centrifugal force is just a psuedo force right? So how is it that in the frame of the table it experiences an outward force? 

According to me it is just like keeping a block on a frictionless table. Causing the table to move would have no effect on the block which would eventually fall off the table because it would eventually run out of table. But here the table is only rotating so no chance of that happening.

Perhaps it's some deep rooted misconception about circular motion .. please help!

EDIT: THE GROOVE IS DIAMETRICAL.