Ancients in the Greco-Roman world were, in general, decent at critical thinking about the past, rather than being more gullible than moderns. For example,...
Historians like Polybius would say rather explicitly that in their culture 1st hand testimony was the primary way to probe into the past.
As one surveys all we know of Greco-Roman culture and their regard for past events, it becomes impossible to deny that they treasured witness testimony above all in trying to ascertain the truth.
• Lysias: “On his stating that he was a Plataean, I asked to what township he belonged, since one of my witnesses there advised me to summon him… I then went and asked at barber's in the street of the Hermae,… and I inquired of such Deceleans… I learnt that… So now, in the first place, I will produce to you as witnesses some Deceleans whom I questioned, and after them the other persons… Relying on this evidence I took proceedings against him before the Polemarch: … I first asked Euthycritus, whom I knew as the oldest citizen of Plataea and whom I supposed to be best informed, whether he knew a certain Pancleon, son of Hipparmodorus, a Plataean. …I went on to ask all the other persons whom I knew as Plataeans. … they told me that I should get the most definite information if I went to the fresh-cheese market on the last day of the month: for on that day in each month the Plataeans collected there. So I went on that day… …I will produce as witnesses Euthycritus whom I questioned first, all the other Plataeans to whom I applied, and the man who said he was this person's master.” [Orations 23-18])
• E.g. Ancients required witnesses in trials. (Examples abound, but see Dionysius for a taste of ancient values re the value of seeing 1st hand1 and witness testimony2 in court contexts.)
Ancients in the Greco-Roman world tended to often quote variations of “eyes are more trustworthy witnesses than ears.” This is relevant because it proverbially praises 1st hand info (seeing vs hearing) while other kinds of info (e.g. old rumor or revelation) were not praised in this manner. And it’s not as if they did not value hearing (or reading).1 So their love of the living voice functions as a fulfilled prediction. While hearing/reading something often meant receiving information merely 3rd , 4th, 5th hand or more, experiencing it 1st hand represented immediate connection with the event or with a witness (his/her testimony) and her authoritative recounting of the event.
Over and above simply valuing 1st hand material more than 2nd hand, and 2nd hand more than 3rd (etc.), Greco-Roman historians around the 1st century tend to find it essentially obligatory that their source-information be 1st hand (or 1st hand as possible). This is relevant because it’s predicted on the hypothesis that testimonies are to be as 1st hand as possible. It’s a coincidence otherwise. For those who allow some lee-way, it clearly wasn’t much.
Regarding most historical works (and writing historical works), there was little desire for the content to be grounded in 1st hand testimony as far as possible. This is relevant because if historians did not even have this desire, then all the more lay ancients in general could not be expected to care.