Technically speaking, you should be allowed to check his deck and hand to ensure no more copies of the card is there.
However as per the post above, thats pertaining to cards which are not restricted. For cards like Dandylion, Critter, then you cannot check.
Similar if for Lonefire he shows you 2 copies to send to out of game then no you cannot check. However if he only shows 1 copy, then you can check for a 2nd copy.
Note though, this is pertaining to the rules that the judge of the tournament that day rules. Typically, you will only be allowed to check his hand, and have to take his word that it is not in the deck.