Being bridged or gated to a WAN does not make a LAN any less of one. This is why many of these arguments don't make sense. The overwhelming majority of residential LANs have internet access, but you'd argue that they then are no longer LANs. Which is silly and completely beside the point.
Purplepaladin's complaint concerning his LAN-party-in-the-woods, I can understand, but that puts him in a minority (Elemental multiplayers) of a minority (on LAN) of a minority (without internet) of players. It's not something most people are going to do--if you're doing a LAN party, you're generally just going to go over to someone's home, and they will most very likely have internet.
All the people arguing "you can't play the game on a LAN!!" or "It's not a LAN if it has an internet connection!" are obfuscating the issues and are doing themselves and us a great disservice here. There are a couple of real complaints here underlying most of them and it'd be a lot more constructive if you simply came out with them directly.
The problem here is basically that there are two camps with differing definitions of what constitutes "supporting MP over LAN".
One definition being used is "no external network connection is required to play MP between two computers on the same LAN", and the other is "it is possible to play MP between two computers on the same LAN".
In my opinion, it is absolutely clear that the first one is the one that is traditionally used.
In my opinion, it is also clear that the second one is generally meaningless.
People may have noticed that there has been a lot of talk in the gaming press about Starcraft 2 not supporting LAN play. Ask yourselves this: Do you really think they mean that it is not possible to play Starcraft 2 *over the internet* with someone that happens to sit on the same local network as you? No. What they mean is that you are required to be connected to Blizzard's servers in order to play multiplayer. This would seem to be a pretty clear indication that at least the gaming press agrees with me about the traditional definition of "LAN play".
As for why the second definition is generally meaningless, ask yourselves this: How many multiplayer-capable games that connect over the internet can you think of that explicitly prohibits two players on the same local network from playing against each other? A distinction that is never relevant is not a very meaningful distinction.
To reiterate, it is my strong opinion that a game that requires internet access in order to play multiplayer does not fall under the traditional definition of what constitutes "supporting MP over LAN".
From Frogboy's posts *in this thread*, it is my understanding that:
1) Elemental will not support MP over LAN at the time of release (though it might at a later time)
2) Frogboy has not stated that Elemental will support MP over LAN at the time of release (he described an easy way to install the game on multiple computers that happen to be in the same location. The later argument about what is/is not LAN play came mostly from *other players* (and you I suppose)).
I should probably also make clear that it is not a problem for me personally that the game will not support MP over LAN at the time of release. I am not likely to be playing the game in a location where internet access is not possible, so for me it just doesn't present a problem. I do however appreciate that others will be playing under different conditions, and I do find the distinction to be meaningful.
Now, you are right that a continued back and forth about what is/is not LAN play is not very constructive, but you could have easily stopped at least that part of the discussion very early on by just coming out and say "Elemental will not support MP LAN at the time of release, but it is something we hope to add at a later time". There would have still been people who would be dissatisfied with the lack of MP LAN, but at least there wouldn't have been as much fighting about what "MP LAN" actually means.
Honestly, coming out and explicitly saying that might still be a good idea.