Just wanted to add my two cents, and it is to agree with what Tristan has said above: If it looks like an all-in, and both players have played the hand as if they are all-in, then I treat the outcome as an all-in and call.
Now, does this situation qualify, and would I take the same approach in cash and tournament?
Had this been a tournament situation and had the two players tabled their hands prior to dealing the turn and river, I would have absoultely paid off the winner as if it had been an all-in situation, and I have done exactly this multiple times in the past.
Had this been a cash game situation, and the players had not tabled their hands (as is often the case with all-ins in cash games) then it becomes trickier. Can we declare that an absence of action is accepted as action itself? Let's look at the (albeit slightly limited) facts:
Player A made large bet, Player B pushed out the entire stack.
Dealer put out the turn and river without further comment or action by either player.
Players exposed their hands.
Now, as a former dealer I can tell you that on a cash game if the bets looked close I would have counted down the stacks to make sure the call was less than the original bet, if it appeared “obvious” that Player B’s call was less than the original bet and was all-in, I would have announced “all-in and call” but would NOT have made the pot right before running out the board. I want to get those hands out, and when two players are heads up and all-in, I will never make the pot right first. As a manager and instructor I will instruct dealers to never make the pot right prior to running out the board in this situation either. Again this is if it is clear that all bets are covered, but by not making pot right first you can push pot to the clearly large stack if he wins and save a lot of time or make pot right if smaller stack wins and take exactly same amount of time as if it was made right before running out board. In this scenario, I believe the dealer assumed that B had a smaller stack size for whatever reason and did like he usually does, but where he failed was to announce the “all-in and call” and had he announced this then the players would have had an extra opportunity to correct the action. Had he announced this and the players did not say anything and let the board be run out, then I definitely would have paid off the winner as if it was an all-in.
In the original poster’s scenario I am still leaning towards and accepted action and call simply because neither player said anything on either street and then turned over their cards at the showdown. Why would they not check on turn or river if they weren’t under the impression that they were all-in? Had one player spoken up prior to the showdown, I would be inclined to allow a bet and option to call on the river, but since the players entered showdown and one players entire stack was across the line, I would rule all-in and call in this scenario.