Okay, just one more... Actually, this is an interesting question and became even more so the deeper we dug. We've heard the same statistic quoted, but not only for Las Vegas, and from our research we're pretty sure the answer to your question is that it's not true.
One problem is the phrasing of the question and whether it refers specifically to churches or to all places of worship, for example? Would Las Vegas' numerous wedding chapels count? While the Wikipedia page dedicated to Las Vegas cites this assertion as a fact about the city, there are several rival locations boasting the same thing, including Memphis, TN, Wheaton, IL, Louisville, KY, Cincinnati, OH, Abilene, TX, and Turlock CA, to name a few we came across, with Wheaton most often cited as the winner.
Founded in the 1830s, this affluent Illinois city has forty-five churches located within the city limits and an additional thirty places of worship in the outlying unincorporated areas. The Genus Edition of Trivial Pursuit states that Wheaton has "more churches per capita than any other town in America." (According to 2000 Census figures, the city had a population of 55,416.)
Evidently, the Las Vegas claim has been around for awhile and was disputed in an interesting article in the Las Vegas Review-Journal back in May, 1997, which posited the theory that this statistic is nothing more than an urban legend, possibly even deliberately propagated by the city itself to counter the seedier side of its image. The 1996 edition of the relocation guide distributed by the Las Vegas Chamber of Commerce apparently stated that, "Las Vegas has more churches per capita than most major cities," for example, although no firm comparative statistics are provided to back up the assertion. Subsequent editions dropped the claim, and the current guide states simply that, "Southern Nevada is home to numerous houses of worship representing over 60 faiths. In all, there are nearly 600 churches, temples and synagogues throughout the valley."
Another interesting source we came across during the course of our research was on a message board at the straightdope.com, where one poster suggested that Centralia, PA probably deserves the accolade of most churches per capita. A once fully occupied coal mining town, it's essentioally been abandoned to an out-of-control underground coal fire that's been raging for decades. While most of the buildings in the town have been demolished, the church is still standing and holds regular services. In 2010 there were still 10 official residents; we're not sure what the figure is now, but it's been declining year-on-year.
If anyone's heard of other U.S. cities that claim the distinction of having most churches per capita, please drop us a line.