President Trump’s recent medical examination was partly theatre: the doctor’s white coat, the “good genes”, the superlatives that seemed prescribed. But it was also serious. This commander-in-chief can personally initiate nuclear war. When the Guardian turned the theatre into audience participation, some readers were troubled. The episode illuminated a recurring aspect of life under the internet – information previously known and used only by specialists is now available for use by almost everyone, without expert understanding of the purposes and limitations of that information. This can discomfort specialists and challenge journalists, who will often be the bridge between experts and a general audience.

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Before Trump’s medical, 75 health professionals urged in an open letter to the presidential physician, Ronny Jackson, that he evaluate the president’s neurological health. “Your examination should also include a basic dementia screen such as the Montreal Cognitive Assessment (Moca), and as thorough a neurological examination as you can perform given your specialty as an internist,” they wrote.

After the medical, Jackson reported that Trump had scored 30 out of 30 on the assessment. A Guardian article reproduced the test questions, which are available on the internet, and invited readers to “take the Trump test” to see if they were “fit to be US president”. The comment thread indicated that some readers took up the suggestion, or had their small children do the test.

Not everyone was smiling. An experienced professional in psychological health emailed the Guardian to point out that our reproduction of the Moca misleadingly suggested that self-administration of the test could be valid, harmed the test’s usefulness by making it widely known, and was likely to needlessly worry those who used the assessment, unaware of the other factors that experts take into account when they employ it to assess cognitive capacity in specific cases.

The relevant editors reflected on the feedback and changed the headline. They also removed the “take the test” element, so that the report simply reproduced the Moca. I think they were right to report the Moca in the first place, but also right to reconsider and amend the context in which the Guardian presented it.

The days of priestly castes of professionals are gone, and mostly for the better

Scrutiny of the US president’s health is plainly in the public interest, and specific reference to the assessment was inevitable after the open letter to Jackson cited it. But context matters, and some media provided more and better detail.

The internet has put into the hands of non-experts much of the knowledge of specialists. In this sense the days of priestly castes of professionals are gone, and mostly for the better. Information flows more freely, strengthening expectations of accountability.

All this presents an ongoing challenge to the mainstream media when the public interest requires that they first find, then understand, interpret and present information generated by specialists.

Willingness of specialists to engage with professional journalists, and the journalists’ openness to feedback and to have second thoughts, are parts of a shared endeavour to serve the public well.

• Paul Chadwick is the Guardian’s readers’ editor