I admit I have not seen it happen where I work, but, the right to do so is there.
To get it for "that good price" on finance, the store has to be advertising that interest free is available at the store of course.
It is also possible that the salesman can simply say, " sorry, that was our last one".
When I sell an item and the customer says,"what is your BEST price"; I have to be prepaired for that customer to say,"OK, I will buy that on finance".

In the end, I do the best I can for all concerned ... make a friend and you will see them again. Likely, their friends too.