There are reasons why people keep secrets. Exposing more of yourself allows better cooperation, but also better attacks.
A partial solution is to expose yourself to your friends, and maybe expose the harmless information to the world, but keep everything else secret. But you need to consider that someone who is friendly (or seems to be friendly) today, may not be friendly tomorrow.
So, the situation with irreversibility is complicated. On one hand, yes, if someone refuses to make a record of their words, you should suspect that they are planning to deny them at some moment in future. (When your boss tells you to do something that seems fishy, but refuses to write it in e-mail or to reply to your e-mail asking for clarification or confirmation, you might consider contacting a lawyer.) A hypothetical perfectly open person would be willing to put everything in writing and post it online.
On the other hand, if there is a good reason to avoid making things public (e.g. to avoid retaliation by a third party), I would expect people to be more open when speaking privately, and more reluctant to write it down, or at least to write non-specifically. Because the alternatives to speaking openly include not just being silent, but also speaking vaguely, or telling a part of the story but avoiding another. So if a good friend writes something vague, I would expect them to be more open if I ask them privately.
If they refuse to write it down even in an encrypted email, or some form of secure communication, then I would say even if they have good reasons to avoid making things public, it would count against the ‘genuineness’. Since it would be very unlikely for their to be any bonafide fears of man in the middle attacks and so on.
The only legitimate reasons would be mistrust between the parties, e.g. fear of accidental or intentional redistribution to third parties, insecure records management, etc,..
I’m not sure if you considered the relative security vs exposu...
There is a book called The Culture Map. It maps behavioral differences across cultures including related to genuineness. For example in cultures with a direct attitude to criticism/feedback you can be more certain that some comment is truthful than in cultures with indirect feedback. (And more so if the comment is harsh)
... And if you don't believe there is one on LW or elsewhere, what what you consider to be the ideal?
'genuineness' here refers to all the positive qualities we associate with the word 'genuine' such as truthfulness, completeness (to their best knowledge at the time of record), fidelity, consistency (with past claims, statements, etc.), logical validity (to the best extent attainable), etc...
My own personal ideal would be something along the following, if no prior track record is available: