I'm wondering if is it possible that the same VISA debit card numbers could ever be issued to different people by different banks or companies?
whilst a card issuer may choose to reuse PAN (long number) to identity a card, a PAN cannot normally be reissued by a different card issuer. The reason for this is because the BIN (first 6 digits) is issued uniquely to a card issuer.
There is one exception: If card issuer is bought by another card issuer (e.g. bank 1 buys bank 2) then card number may be reissued under the new name of the card issuing organisation - but really this is an edge condition and in the spirit of the question the answer is largely no
Note: In the UK, Clydesdale reissued mastercard PANs, but eventually stopped after obvious problems occurred. see: http://www.theguardian.com/money/2003/may/10/creditcards.debt1