So when a midday rumor began to spread like wildfire inside the media room at the Opryland Hotel on Tuesday, a proposed trade that included Lee, Amaro was quick to squash it like an unlucky bug crawling under the bottom of his loafers.
"That would be incorrect and false," Amaro said of a tweet from ESPN's Pedro Gomez that had the Phils talking to Arizona about a Lee-for-Justin Upton swap. "I don't know where that would come from, but as you all well know, there's a lot of falsehoods out there. And that's absolutely one of them."
And so on the second day of baseball's winter meetings, the Phillies remained the quietest team in the building.
Former Phillie Shane Victorino became the third free-agent centerfielder in the last week to find a new home when he agreed to an eye-popping, 3-year, $39 million deal to join the retooling Boston Red Sox on Tuesday. The Phils' interest in Victorino was mild at best.
And given that price tag, perhaps nonexistent.
But ever since the Phils traded Victorino in July they've had a void in centerfield. And the most natural centerfielder on the 40-man roster is Tyson Gillies, an oft-injured 24-year-old with zero major league experience who has played in just 106 minor league games since being acquired in the aforementioned Lee trade.
Despite an obvious need for a centerfielder and options literally dwindling by the day, Amaro has kept his cool in Nashville, refusing to make a rash move and instead practicing patience. And that patience may very well have to continue for a while longer.
"When these guys go off the [free-agent] board . . . my feeling is the domino effect is now a player that might be available in a trade, his value goes up," Amaro said. "And so teams are going to want an extra prospect or player for a guy, or a stronger package of players. Money can affect some of the things you can do on the trade front as well. That may delay some things. Teams that have a surplus or are willing to move a quality player, the asking price is high right now and we may have to wait for it to come down."
Although Amaro could very likely add two starting outfielders this winter, he may not make the first move until January. Or he could make it before the Phillies' brass leaves Nashville on Thursday morning.
Amaro generally plays everything close to the vest, but he did admit that the climate for making deals could change every half-hour. Despite not having anything to show for it, Amaro said he "had a lot of interesting discussions with free agents and other clubs" on Tuesday.
"It was an encouraging day because there are some things out there that I like," Amaro said.
Could it lead to something in Nashville?
"I guess it's possible, judging from some of the dialogue. But just like in any other situation, there are ebbs and flows. One day you think you have a deal done, and 30 minutes later it's off. When you say, 'Are you close to something,' close doesn't mean [squat]."
What the Phillies are not close to is trading Lee. So, if nothing else, antsy Phils fans can avoid hyperventilating as they comb through the latest barrage of trade rumors circulating in Nashville.
In attempting to fix what ails his aging, injury-plagued, underachieving team, Amaro has no plans to subtract from the core of former All-Stars, Cy Young winners and MVPs.
"I think our best chances are to keep the core together," Amaro said. "Our best chance to win is to keep the core together and healthy. So probably not. We're probably not going to move any of the core players on our club because I think it would just weaken us too much. I don't think we'd get the value that we would need if we moved any of those guys to make us a better club necessarily."
Even with steady movement of free agents to new homes in the last week, the two highest-profiled outfielders - Michael Bourn and Josh Hamilton - remain unsigned.