Although United and American probably do have an interline baggage agreement (most of the larger IATA members do), and are probably capable legally and operationally of transferring bags directly, it is up to the discretion of each airline whether or not to do so. And most US carriers have been increasingly reluctant to do so over the last few years as they have collected more of their revenue from baggage fees.
Thirty years ago, when airlines were much smaller, there were no alliances and few express carriers, and the major carriers mostly operated on a high-cost, high-revenue business model, bag interlining was common, and done as both a courtesy and a necessity. Nowadays, fewer passengers need to interline, and more importantly, baggage fees have become an important part of an airline's revenue.
In 2011 and 2012, the US Department of Transportation handed down new regulations relating to baggage fees; to prevent passengers from having to pay multiple sets of baggage fees and manage multiple sets of baggage allowances, over a multi-carrier itinerary, they would only pay one fee and get one allowance. That introduces a risk that a carrier might not collect as much in fees as it could; by refusing to check in a bag for an entire itinerary, it can still collect the maximum. Thus, this was the proximate excuse for airlines to make interlining bags more difficult. Some, like Alaska and Delta, backed down in light of furious consumer protests; others, like Hawaiian and US Airways, stuck it out. I haven't uncovered anything specific about American or United on this particular issue, but in light of the shift in the industry, it wouldn't surprise me that they are moving to limit interlining operationally, if not a matter of announced policy.