Not sure that is correct but its a moot point.
You can not be sure all you like, but you are wrong. Parliament can (and has) enacted both advisory and binding referendums - indeed the last 2 all UK referendums have been one of each. Had parliament chosen they could have enacted a binding referendum on brexit - they chose not to, rather they enacted an advisory referendum, which by definition mustn't fetter the discretion of parliament to decide or not to implement the results of the referendum. So once again the exact wording from the official briefing notes on the bill.
'This Bill requires a referendum to be held on the question of the UK’s continued membership of the European Union (EU) before the end of 2017. It does not contain any requirement for the UK Government to implement the results of the referendum, nor set a time limit by which a vote to leave the EU should be implemented.'
And the point as to whether is was advisory or binding, or whether it could have been the latter, isn't moot - indeed constitutionally it is critical. Either parliament os sovereign or it isn't - it you try to make a referendum that parliament has chosen to be advisory effectively binding (by trying to require them to implement the result) then you have curtailed parliamentary sovereignty.