I think the truthfulness of the information you get hinges on how much connections you have. If you’re not that well connected, you have only the references given as a source of information, or the principals, neighbors, or friends, etc of the single. Generally speaking, unless these people know you, they arent going to tell you anything negative. OTOH of you get someone you know well, who either knows the person they’re asking the questions of well, or has “muscle” in the community, to inquire, more chance you’ll get the inside scoop.
If 2 people, one a stranger, one an acquaintance, ask the same person, the same question, they often get a modified answer.
As far as Dor Yesharim, no one Litvish I’ve dealt with checks before a fourth date, and it seems strange for one side to ask for the other’s numbers before then, for that reason. For some reason, the more modern the crowd, the later they check. Possibly because each additional date, isnt of such major importance bec they go out with many more people.