Different redeemScript for the same scriptPubKey?
A P2SH transaction will execute whatever redeemScript you provide, which must be a standard transaction:


  Transactions that redeem these pay-to-script outpoints are only
  considered standard if the serialized script - also referred to as the
  redeemScript - is, itself, one of the other standard transaction
  types. See BIP16


Those standard transactions, like a P2PKH does require a signature, so even though you provide the right redeemScript, if it doesn't execute successfully, the entire tx will become invalid.