We only have Harry that said these texts said x,y,z. I think it’s been shown the book is full of inaccuracies, so his account can’t be trusted.
however, even if we are to take that these words have been said, we don’t know if he is quoting the full text message, part of the text message, or all the messages regarding the fittings
For example:
kate could have wrote in her final text message where she supposedly have said a curt ‘ok’
She could have wrote ‘ ok, will go round this morning and get everything sorted’
Technically, Harry wouldn't lying, he would just be quoting part of a text. He also wouldn’t be changing the meaning of the text. But what it could do is change the tone of the exchange. We don’t actually see a picture of the text exchange.
Harry’s version of events aren’t to be trusted