I wish people would stop saying that. It's just not true.
Some Liquidmetal alloys are based on platinum and some are based on much less expensive materials. The most common alloy is under $15 per pound:
(The original article link is broken, but someone in this thread states:
"The article quotes a price of $12 - $15 per pound for the liquid metal, versus $6 - $15 per pound for titanium."
That is consistent with what we know. They make golf clubs and reasonably priced tennis rackets (under $60) from this stuff (although the tennis racket only has small pieces of LM). If they're making $60 tennis rackets using LM, there's no reason a $600 phone couldn't use it.
Let's explore. Let's say that the iPhone's backplate has 1 ounce of aluminum and you can replace that with double the weight of LM. So you've got $2 worth of LM in your iPhone. WORST CASE, your manufacturing cost goes up by 1%. However, Liquidmetal products are manufactured by injection molding rather than machining so there will be savings on machining cost. That would reduce (and maybe even eliminate) the cost differential. And it's certainly nothing like the cost of silver or gold (not to mention the fact that both of those metals are too soft to be the backplate for a phone unless you alloy them very heavily).
I strongly suspect that the reason it hasn't appeared in an iPhone yet is that Apple is still working out the manufacturing issues involved in making millions of pieces from this material. From talking with LM's engineers for a different project, creating a high volume manufacturing process is tricky and there are still some bugs to be resolved. The SIM ejector tools that Apple included in previous iPhones was presumably an experiment to get some experience working with the metal. There was no reason other than that.