I don't think there is any ambiguity in the wording of Robert's Rules. If there has been action on a board card, the card must stand. The idea of "substantial action" originated from rules on (pre-flop) misdeals, I believe, which is a wholly different type of scenario. Now, would it be nice and convenient if we simply applied the definition of substantial action to other situations? Maybe. But it's the lazy way out, IMO.
I should point out that the original post dealt with the dealing of premature board cards, as well as no burn/multiple burn situations. For the reasons Tristan gave, allowing a reshuffle if someone has acted on an improperly dealt board card, but when there technically has not been "substantial" action is plain wrong, and not within the spirit or the language of the original rule.
A related, but also different situation is when a player was skipped within a betting round. When does a skipped player lose the right to act? After any action? After substantial action? We discussed this in another thread. I think most of you are leaning towards applying "substantial action" in these situations (which I don't like but I can support), but let's recognize this is a different scenario altogether, so let's not assume that it should be treated the same as premature dealing of board cards.
In my original reply, I set out what I think is the current standard for dealing with these types of situations. BUT, if it were up to me, I would implement a rule that results in less reshuffling. This entails not trying to fit in the dealer's burn and turn into the definition of substantial action. At least not as one of the "actions" involving or not involving chips. I think it unnecessarily muddies the definition of substantial action.
In my personal view, the dealer dealing a new street is a key event that should have its own significance. If a dealer deals a new street, all action up until that point should stand unless an irregularity is brought to the attention of the table without delay. This means that once that 'fence post' is passed, I think play should stand unless there are extenuating circumstances.
I feel the old Robert's Rules formulation that the current standard is based on is way too liberal - namely that anytime action from the previous street was not complete, we need to reshuffle. Sure, sometimes a reshuffle is warranted if the dealer truly made an error by dealing the next street prematurely AND there was no delay by the skipped player in trying to stop it... But in most cases, when the dealer properly collects the chips, announces the number of players, taps the felt, and burns a card, this is more than sufficient warning for anyone to say something.
So if I had my way, I would say that if a new street is dealt, the presumption is that any player who had not yet acted on the previous round of betting is deemed to have either checked, or folded if facing a bet. Sorry, if you were missed, you've lost your chance. Now, if you had a turbo dealer and you spoke up as soon as you thought you were being missed, I might apply Rule 1, but that should be the rare exception and not the norm, especially when it comes to a premature flop. (I really, really do not like redealing flops, and with all the dealer's actions that precedes the dealing of the flop, there really is plenty of time to speak up).
Right now, the rules do not explicitly give the dealer's tap and burn such importance and distinct status. But I think they should, and I do not think we need to touch the definition of substantial action to make it happen.