Yet in this age of celebrity feuds -- an area where Trump has clearly emerged as a standard-bearer -- he just might have been crazy like a fox.
After all, if you're going to pick fights for maximum exposure and impact, the leader of the free world seems like the perfect choice to suit a Trump-sized ego, which has spread such spats into his disparate worlds of entertainment, business and politics.
The Trump modus operandi becomes crystal clear watching the March 3 premiere of the latest "Celebrity Apprentice," an "all-star" edition (if that's not an oxymoron) where the squeakiest wheels get the grease. Even judge Piers Morgan -- a past winner of the competition -- engages in plenty of petty sniping with contestant Omarosa Manigault-Stallworth, with whom he clashed when they were contestants together.
The verbally pugilistic participants appear to be borrowing a page directly from the Trump playbook, which has included past exchanges with the likes of Rosie O'Donnell, Cher, MSNBC's Lawrence O'Donnell and attorney Gloria Allred. More recently, Trump filed a lawsuit against Bill Maher -- motivated by a joke the HBO host told about Trump proving his own origins (to Maher, his hair color suggested an Orangutan might be involved), as Trump had asked President Obama to do. The suit left Maher to quip on his show "Real Time" that the comic's lawyers urged him not to respond "until they stop laughing their asses off."
One of the obvious reasons feuding has become so popular is that it's easier than ever for the world to enjoy a front-row seat. Once, stars would have had to find a pliant reporter willing to transcribe and publish their puerile insults. Today, they can lob them filter-free via Facebook or Twitter, the latter perfectly designed to accommodate pithy bursts that amount to not much more than schoolyard taunts.
The media also has a near-unquenchable appetite for two central aspects of these feuds: celebrity, and conflict-as-spectator-sport. The old expression "Let's you and him fight" comes to mind.
In this context, it doesn't take much to get websites to elevate snarky tweets between, say, New York Times number-cruncher Nate Silver and a Politico reporter to a full-fledged "feud," or US Weekly to promote the backstage rivalries viewers missed at the Grammys.
With his flair for self-promotion and a naturally combative nature, Trump has tapped into this national dive into provocation, perhaps as much intuitively as consciously. At times, the Trump philosophy appears to be, "I feud, therefore I am."
Still, those who have asked whether Trump's carping about Obama could somehow become a source of embarrassment to NBC -- a network desperate for a little ratings traction -- have missed the point.
Faced with the challenge of knifing through media clutter, practically anything that generates attention is potentially helpful. Publicists who previously sought to steer clients away from mudslinging and controversy today can almost be seen invisibly guiding made-for-TV personalities like the Kardashians from one manufactured crisis to the next.
A Web culture with few qualms about hyperbolic headlines (the Huffington Post is a master in this regard) has also played a central role in inflating modest disagreements to "feud" status. And reflecting the country's ideological polarization, partisan cable hosts have made cross-network sniping part of their daily routines.
Admittedly, there's not much real harm in these theatrics and histrionics, except perhaps in the way more artful and experienced feuders manipulate the media, which pounce on these momentary flare-ups with little regard for whether there's any genuine anger involved or if this is just the equivalent of professional wrestling.
Not that Americans can be relied upon to know much about the past, but it's telling that the History channel set ratings records in May with the miniseries "Hatfields & McCoys," the family vendetta that played out over decades in 19th-century Kentucky and West Virginia.
Now that was a true feud. And one can only imagine the additional damage those warring clans might have done if, like Donald Trump, they had access to Twitter.
© 2013 Variety Media, LLC, a subsidiary of Penske Business Media. All rights reserved.