Learn English – what is the word that describes someone who keeps their real personality secret

As the commenters on the question note, your examples seem just to show people saying harsh things-- perhaps they misspoke, or regretted their words as soon as they spoke them, but language is founded on the assumption that we mean what we say and say what we mean.

There are cases where what one fails to say can cast an otherwise innocuous statement in a negative light. If I ask "did I seem like a stammering cretin in that meeting?" and you reply "I didn't notice you stammering", that implies you did think I was a cretin, even though you didn't say that and may not have meant it. This is usually referred to as "damning with faint praise".

You're looking for "axiom", a statement that is regarded as being established, accepted, or self-evidently true.

• axiom (noun) A self-evident or universally recognized truth; a maxim "It is an economic axiom as old as the hills that goods and services can be paid for only with goods and services" (Albert Jay Nock). TFD

• axiomatic (adj) relating to or resembling an axiom; self-evident