Is Budweiser really the most expensive beer to brew? On bottles of Budweiser it claims that:


  We know of no brand produced by any other brewer which costs so much to brew and age. 


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This seems implausible both from the point of view of economics (it’s brewed in enormous quantities and sold cheaply), and given it doesn’t involve any special additional ingredients, ageing, or hand production. Why do they claim this and how are they allowed to? 

Note: I can see that it may hinge on what “brew”, “know”, “producer” means but unlike, for example “possibly the best beer in the world....” , it makes an objective claim.
The answer may be in the question you asked:


  it’s brewed in enormous quantities


If you look at the aggregate cost, it is indeed almost certainly the most expensive beer in the world to brew and age, because they make so much of it. The total cost for brewing Budweiser probably far exceeds the cost of brewing any other single recipe, year over year. 

Per bottle, however is a different story.  Budweiser isn't particularly cheap, from a bill of materials perspective, but it isn't exceptionally expensive either.  However when it was introduced, it was extremely expensive.  At retail it cost the equivalent of $17 a bottle today. The cost savings today are largely due to efficiencies in integration, scale, and processes.  

So is it still true that it's the most expensive beer to produce today?  On a per bottle basis, certainly not.  That doesn't mean, however, that they're cutting corners on production, but as the comments noted, simply taking whatever legal liberties are available to them when making that claim.