I had that coming.
That’s the point — I’m from California. For me, “porn” has the same [r] sound as “rain.” Also, “pawn” has the same vowel as “pond,” which is not the case for Brits. In Britain, the [r] in “porn” is weak to the point of non-existence. It isn’t so much a consonant as a rhotic coloring of the vowel. Since neither their /aw/ nor their /or/ exactly matches anything in my dialect, I hear them both as /o/ and I can’t hear the distinction between them. British people have no trouble making it: I tested.
Where were these British people from? I have a RP-ish British accent, and I pronounce those two words exactly the same.
Both from Wales, one from Anglesey (natively bilingual with Welsh) and one from South Wales (monolingual English), slight Welsh accent. Note that Welsh has rolled [r] and aspirated rolled [r] but nothing like English [r] or British rhotacized vowels.
I roped an Irish housemate in to help me observe and made the Welsh people do “blind” (deaf?) tests: one person would leave, and the other would be told which of the two words was to be used. We did this a few times and then swapped. Although I was listening closely, I could never hear a difference, while they were right 100% of the time. They were both puzzled by my inability to make (to them) an obvious distinction, and had no reason to deceive me. One of them is my partner, and in the years since I’ve never had any occasion to doubt the conclusions. Of course, I still can’t hear the difference between British par and paw, so what do I know?
Or me (Northeast US) 
Aha! The haughty-hottie merger!
ETA: pawned-pond itself being another minimal pair in that vein.
Lifetime Ohioan here; I would pronounce haughty/hottie and pawned/pond the same. But I’m still waiting for actual examples of the Midwestern “R” sound that the OP puzzles over.
I think he means in contradistinction to the so-called guttural R of French and the trilled R of Spanish.
As far as being a distinctly American feature, I suspect it is because the non-rhoticity of RP was taken to mean that the /r/ is never pronounced, when in fact it is only suppressed in the syllable coda. Thus an RP speaker and a GA speaker would pronounce the r’s in “Ronald Reagan” in the same way (that is, as alveolar approximants).
lager/logger are two that I do pronounce the same, but yeah, all the others in the list are analogous.
Kimmy_Gibbler, can I just say that I’m awed by the clarity of your posts? (I took something you said the wrong way in another thread, once, so if I can hijack for a minute I’d like to apologize.)
As others have said, when the OP is talking about the American “r,” it seems to mean only post-vocalic [r]. Take the word roar. The initial r- is the same in both RP British and Midwestern American. The final -r is different in the two dialects. I think the OP is referring only to the latter, even though it’s technically the same sound. In other words, not all [r] sounds in American English, only some of them, the ones that are distinct from other dialects and therefore noticeable.