We first find out about the gold from Friedrich on Happy Happy, Carnage Carnage. In reply to the name "Walter" Friedrich says:

Muller gave Walter a gold key and sent him
to recover a large amount of gold and a
strange wooden box.

If you enquire further about the "gold" or the "gold key" Friedrich reveals:

Muller maintained that there was some
reason we needed the gold- other than his
greed- but I never quite believed him.

Dustin Westphal <bachus@rdc-cybersign.com> takes up the story:

Muller will respond to the word "gold":

I gave Walter a gold key, and told him he
was looking for a fortune in gold, but I was
only appealing to his sense of greed. There
is no gold.

We know that Muller lies through his teeth, but what exactly is the lie here? Walter on Feel The Power tells us that Muller knew of the gold, and of course the gold clearly exists. So why would he lie to us about there being no gold?

Walter says:

Muller said we needed all twelve ingots, but
that the box would duplicate things which
were placed inside it so we should only get
one. We found the box.

And:

Muller sent us to get one gold ingot and a wooden
box, he said they were extremely important.
I was leaving though, there was no way I
was going back down to try to find him.

And Friedrich says:

Muller maintained that there was some
reason we needed the gold- other than his
greed- but I never quite believed him.

Does this make sense to anyone else? Muller clearly thought that the gold was absolutely essential. Yet Muller doesn't want us to know about the gold. He says it doesn't exist. Why are the ingots so necessary anyway? They seem to serve no purpose other than to give you a better score at the end of the game. Was there originally supposed to be a puzzle in which 12 gold ingots would be needed? And as another mystery, why did Walter take only one ingot? If I was in a room with twelve ingots, I would take all I could carry. Not just one. It seems like Walter tried the cedar box at least once, and he knew that the ingots wouldn't fit inside. Why didn't the greedy git go back and get the rest of the gold?

Dustin makes an interesting observation about the twelve gold ingots. Did they serve some other purpose other than treasure? Let's review the evidence again.

For some reason Muller explicitly denies the existence of the gold but oddly not the vial or the wooden box. Why deny one thing yet not other seemingly more important items?

Friedrich tells us that Muller needed the gold for some reason other than greed.

Muller maintained that there was some
reason we needed the gold- other than his
greed- but I never quite believed him.

Walter's remarks are also interesting. First Walter says:

Muller sent us to get one gold ingot and a wooden
box, he said they were extremely important.
I was leaving though, there was no way I
was going back down to try to find him.

But when you ask him about the wooden box he says:

Muller said we needed all twelve ingots, but
that the box would duplicate things which
were placed inside it so we should only get
one. We found the box.

So Muller needed all twelve ingots yet Walter was told to get only one. Of course if Muller thought that the box would duplicate the ingots then one would be sufficient to create the other eleven. However the ingots won't fit inside the box as Walter found out:

The box worked like he said, but the ingots
wouldn't fit inside it. I dropped it when I
was attacked by the invisible demons, it
was useless. But I kept the ingot.

So why would Muller need twelve ingots for a reason other than greed?

Apart from being valuable ($38,000 each) the ingots are also extremely heavy. Each ingot weighs 13.04kg and all twelve weigh 156.48kg (345lb). That's an enormous load to carry particularly when you add the weight of all the other items in your inventory. The issue of weight has been raised in the The Red Velvet Bag section. It was noted that the game's weight warning dialog:

"You're so encumbered with objects that you can't move. Try dropping something heavy."

wasn't implimented in the final release. Thus it is possible to carry an unrealistically heavy load during gameplay. It was also noted that the Red Velvet Bag has the ability to make any item placed inside it appear weightless. Thus if the game's weight warning dialog had been implimented one solution to the excess weight problem would have been to put the gold ingots inside the Red Velvet Bag.

Was it the weight of the ingots that was important to Muller? Were they needed to trigger some weight sensitive mechanism inside the pyramid? A weight puzzle that required recovering the twelve gold ingots, then using the Red Velvet Bag to carry them, and finally using their combined weight to trigger some weight sensitive mechanism?

Ah the Mystery of the Gold. Will the tru7h ever be revealed? ;-)