Under the law, by which all things count whether private or council land, if you have not "parked with the intention to defraud" and therefore have a paid ticket then you will win the case in court, certainly. If the ticket fell onto the floor then you can claim that you put it on the dash and wind from the vents blew it off (an external gust will travel through to the vents). It is IMPOSSIBLE to prove you wilfully failed to display the ticket when you have proven intent to "pay and display" with the possession of a parking voucher/receipt - hence the legal contract of "pay and display". If the private company tried to play bully boy then tell them you will take them to court - you paid your ticket, end of! If they think you're talking crap, ask them if they can prove you did not display the ticket. When they fail to logically do that (which they will fail to do) simply say "I won't pay it, take me to court and I'll let you pay the costs and lose them!"
Do not get into pointless arguments with them, just let them take you to court. Remember, Penalty notices on private lands are not in any way as enforceable as are council parking tickets. On private land, once you cross the land's perimeter you automatically enter into a contract to pay for the space you occupy. You did, so end of: you fulfilled your contractual obligations. "Pay & Display" is a collective legal term and you cannot easily prove one without the other. The legal bods among us we'll confirm that it is "assumed" that when you paid for the ticket (you have it) that you would thereafter naturally display it."
