This implies that you do have a statement which shows a purchase for a
greater value of goods than the cost of the drill. If this is the case
then take this and ask again for your replacement product. You may not
be able to prove that this was the transaction on which you purchased
the drill but equally they cannot prove that you didn't and you have
made reaonable efforts to provide them with the proof they have asked
for. The fact that you are not asking for a refund usually makes these
things easier. I agree with other comments here, you were unlucky with
the individual you were dealing with and on a different day you
probably would have got a replacement without any hassle.