I actually didn’t notice it myself (at least not consciously); I was just making a random joke. Now that you point it out, it does look a little odd, but not enough to convince me of anything.
As is usually the case with these kinds of discussions, the problem is that if your dialect features the Mary-merry-marry merger (as mine does), then Carey, Kerry, and Carrie also sound exactly the same.
Folks, let me clear up some confusion: the word “American” was prominently mentioned in the OP to prevent British and Canadian posters from offering their own ideas about pronunciation. While I appreciate their input, this question is strictly about the US and the American accent. As you probably saw someone already posted a British answer and I’m not interested in that.
Thanks
Funny enough, there’s a thread here on Talkbass.com discussing the pronunciation. Of the people who answered one way or another and not one of the non-answered, 4 pronounced it “burry” and 48 “berry.” However, if you read through the comments, one of the “burry” pronciations is from Maryland (“Burr-e. I never thought of myself as a southerner but I suppose Maryland does run under the Mason-Dixon Line :D.”) He’s from Mitchellville, though, so closer to DC.
As well as Ferry / Fairy, Hairy / Harry, etc. Although I HAVE heard the alternate “burry” pronunciation - but that’s a different issue. I think of that as sort of a “folksy” or “rustic” way of pronouncing the word. I might actually use it for rhetorical effect.
“My hairy uncle Harry married Mary, and left on the Ferry” - all the same bloody phoneme the way I pronounce it. And when I listen to examples of them being pronounced differently, they STILL register as the same phoneme. Oh, if you point it out I can tell there’s a difference, but all of those sounds are just interchangeable variations on the same phoneme as far as I’m concerned.
“Dawn” and “Don” are vastly different, though …
Yep. The weird part is a friend who is caught (not cot) in the merger but also can’t hear the difference even when I pronounce it right in front of his face. It’s like he can’t even process the different sounds…
I mentioned Mary/marry/merry because even though I pronounce all three of those differently, I do merge berry and bury. Not sure why.
Your OP proceeds from a false premise: that there is an American pronunciation. There are several. So the restriction is shot from the get-go.
To closely answer the restricted hypothetical: mu. Or perhaps, “not even wrong.”
The only way for the conversation can really proceed is on the terms it already has: the variety of equally valid regional pronunciation of the subject word, plus the related family of words with similar vowel drift dynamics.
Yep, if your dialect doesn’t differentiate a sound, then it’s very hard for you to even hear it. I tell the story about when I was in Germany and asked a fluent German speaker how to pronounce the name of the beer I was drinking: Koenig (actually it had the umlaut-o, but I don’t know how to type that). According to my perception, he said “koo-nig” to which I replied “koo-nig.” He said “No, koo-nig.” So I said “koo-nig.” He said “No, listen closely: koo-nig.” So I said “koo-nig.”
We went through this several times before he described how what he was saying was different, that he would hold his lips in a different position that if he were saying the “oo” sound.
I am very close to being the same way. I find it very difficult to hear a difference, even when people are supposedly exaggerating the pronunciation in order to illustrate the difference! 
That’s just how these things work.
The only time that I’ve ever managed to hear a difference “on my own,” so to speak, was when I was watching an old episode of The Mary Tyler Moore Show. At one point, both Mary and then Rhoda spoke the sentence, “Why aren’t you married, Mary?” Hearing both words in immediate proximity like that, I did hear a difference in pronunciation. But usually I can’t.
Now cot versus caught, on the other hand–those sound completely different!
I felt like Chris Tucker: Do you understand the words that are coming out of my mouth?!
Look! Just look at how my mouth is shaped different!!
Cot/caught – I’m glad we have some common ground. 
Huh. I’ve somehow gone my entire life believing that “berry” was a “hick” pronunciation, like “warsh”.
I think this is an African-American thing. Think of Charles Barkley (though I’ve heard black folk in the south say “burry” too).
Maybe he didn’t want people to think he was talking about himself in the third person.
So you were looking down on people as they were looking down on you?
The “r” seems to alter both perception and pronunciation of these vowels for speakers that merge Mary/merry/marry. I have a few comparisons that may help make the differences clearer.
Consider the vowels in ale, el*, and Al. Or sale, sell, Sal. If you merge Mary/merry/**marry **but distinguish three separate vowels in sale/sell/Sal, you can use your knowledge of the latter three to understand how other speakers distinguish the former three.
No value judgment intended – all pronunciations given in this thread are equally legitimate. Since I merge Mary/**merry **(but not marry, go figure) in my native dialect, I 've only learned in recent years that the way some people distinguish Mary from the other two is with a vowel that yields something that sounds to me a little like “May-ree” – close to the vowel in ale and sale.
*as in "the letter ‘el’ [L]"
.
All I know is the humor of “Harry Johnson” is lost on me.
Whoa…“Social milieu by M.C. Escher”…
And I’m from Salisbury, MD. Everyone pronounces it Salsberry.
Great post. I hear/say all 3 different and your analysis of Mary/ale is spot on.