Most of us will have had the experience of mentioning some well-known phonetic feature of a given language/dialect/accent, only to have a native speaker deny that any such thing occurs.
I might point out to my phonetically unsophisticated audience that in words like bad, which in Britain ranges generally in the area bæd ~ bad, Americans often pronounce something with a much closer vowel, perhaps nasalized, often with an off-glide, something like bẽəd. Brits nod their heads in agreement. But a kindly middle-aged American lady protests that she has never heard such a thing: Americans never use such an ugly pronunciation.
Or, talking to a British audience, I mention the phenomenon of smoothing, whereby for example science, notionally ˈsaɪəns, is often/usually pronounced without any kind of phonetic ɪ in the middle, just ˈsaəns ~ saːns. People protest that they would never do that themselves, although they admit that perhaps effete upper-class/vulgar lower-class people might sometimes do so.
So it is with American t-voicing. You point out that atom and Adam are (usually) homophones in AmE. Oh no, says an American, that’s not true. Indeed, when Webster’s Third International (1961) pioneered the idea that the intervocalic consonant in this word is d, this was not well received in the United States. To this day, another dictionary from the same stable, Webster’s Collegiate, tells you that this word is pronounced with t. (OK, given that the t ~ d contrast is typically neutralized here, it may be reasonable to continue to write it as t. Arguably, the adjective atomic, where the t remains voiceless, enables even illiterate speakers to know that the underlying consonant is t, not d.) More sophisticated Americans will tell you that some distinction of vowel length or vowel quality enables the distinction to be preserved in such words despite the voicing of the obstruent. Indeed, this is why in LPD I felt obliged to fudge the issue by using a special voiced-t symbol. But the ODP, to its credit, gives the AmE pronunciation of atom as ˈædəm, with no further options.
Likewise with American nt-reduction. In the positions where AmE has t-voicing, many Americans reduce historical nt to plain n. This makes winter a homophone of winner ˈwɪnɚ and dental ˈdɛnl̩ ~ ˈdɪnl̩ a rhyme for fennel.
If your audience are reluctant to trust the evidence of their own ears when you play them sound clips of people using the pronunciations you are talking about, they may be convinced by the visual evidence of spelling mistakes.
I came across a particularly neat example of a spelling mistake based on nt-reduction. Shumway “Innernational” Airport, located in Shumway, Illinois, has its own Facebook page.
Actually, though, given that the reported population of Shumway is just 202, I suspect that the whole thing is a spoof. But there are 56,800 Google hits for innernational.