"It's probably not the greatest thing for Amazon shareholders" for Bezos to own the paper, said Graham, who covers Amazon at financial firm Canaccord Genuity. "It definitely makes Mr. Bezos a lightning rod for what's going on politically."
The Washington Post and Amazon have been frequent punching bags for Trump, with the president blasting them last month in a barrage of tweets, including accusing the paper of being Amazon's "chief lobbyist," and saying Amazon is taking advantage of U.S. taxpayers.
"The president is trying to fight back with every means available" against what he considers unfair treatment by the media, Graham said in a "Squawk Box" interview. "They're partially political. I think they're partially, sort of, well-placed in terms of trying to make sure Amazon is paying their fair share of taxes."
The Post-Trump distractions are not major issues in terms of Bezos' greater vision for Amazon as a leader in e-commerce and cloud computing through Amazon Web Services, said Graham, who has a buy rating on Amazon. He upped his price target last month to $1,800 per share based on, what he wrote in a note to clients, "a sum-of-the-parts analysis on 2019 estimates."
Amazon has surged nearly 40 percent year to date, closing Wednesday around $1,625. A move to $1,800 would represent a 10 percent increase and a market value approaching $900 billion.
AWS is "for now" subsidizing Amazon's retail business, said Graham. "AWS is clearly helping the stock, which is helping the company operate."
Amazon is doing something similar to Walmart but also "losing money at it," Simon said. "They're gaining traction and profitability by other business activities that have nothing to do with retail."
Graham said Amazon is running its retail business at breakeven. "They're doing that on purpose because the whole name of the game is 'let's ramp up the delivery capabilities as fast as possible.'" He added, "International [retail] is losing money. The U.S. is making a little money."
However, Graham said there's nothing sinister going on. "I think they would be running the e-commerce business the same way regardless if they had AWS or not."
The 54-year-old Bezos, the richest person in the world with a net worth of $134 billion, started Amazon 24 years ago with the idea of creating an online bookstore. In addition to owning The Washington Post, Bezos also started the Blue Origin commercial space company.