All of these points would be valid if you assume Semirhage had an elaborate plan set up to sow dissent on the off chance that someone would ask Rand how he could identify her if her illusion was unravelled.

What really happened is that she answered on the spur of the moment. Combined with this, the chapter can be summarized like this...
1. She says that Graendal knows more of the mind than she does, which is true from what we know of these two Forsaken.
2. She says that Graendal spoke about reintegration in detail - of which we have hints from the Prologue of FoH.
3. She says that Lanfear always said Rand knew things from the AOL that only Lews Therin knew, which we all know is true.
4. Lews Therin knew Semirhage and says she rarely lies, which is a dumb thing for them to write if it's also a lie.
5. Rand is mad. Even Jason's spoiler-free review states that this new book shows Rand's descent into terminal madness. if anything this validates Semirhage's opinion.
6. Semirhage's rare lying is seen in every chapter we have on her. She is ruled by calm and logic, and there are no falsehoods in her chapters.

I'm not saying Semirhage cannot lie, or will not, nor do I have the mad need to trust this woman, but I posted long ago on wotmania that her statement in KoD is completely true. We know it's true. Even Rand thinks it's true and it's from his own PoV! Lews Therin stating that she tends to tell the truth (a remarkable virtue for a Forsaken) merely proves my point further.