I do think Shallan might be more of a special case, She had bonded and spoken truths before her mother tried to murder her, so it may specifically be her circumstances that make it more difficult for her, not the Order itself. I'd like to imagine a Lightweaver speaking truths that they want to deny, but aren't tied to traumatic experiences ("I am a skilled liar, no matter how much I hate it", "I do not believe in the edicts of my homeland", or something like that). These people are still speaking personal truths, but in these cases, it would be acknowledging an internal struggle, not a trauma.