Itchy the cold reading 'evidence' tends to be way more general than the type of evidence that is truly incontrovertible to the sitter.
When spirit are able to speak to their loved ones still here, often the first thing they want to say is how much they love them. While this is lovely to hear - and ultimately the whole point of why the individual has come for a sitting - it doesn't, of course, prove anything in itself. However, if they can maintain the connection with the medium, often what follows is more evidential. Sometimes it can be a specific piece of information that clinches it for the sitter, sometime it can be an accummulation of things that, taken together, add up to the sitter knowing it is really the person they hoped to hear from.
I once, while sitting in a development circle, got a link with the husband of the person i was practising on, and he told me something I would never in a million years have thought to say, yet it was extremely evidential to the sitter. The man in spirit had been a singer songwriter, quite famous within his own niche, but not within the mainstream. I had never heard of him or his music, as I am not interested in the genre, and it was 30 years before my time. He told me to say a phrase that sounded fairly innocuous, but strange to say to a woman. He was insistent I say it verbatim, though I was sure I must have misheard. In the end, I just said what I was hearing, to be told it was very evidential, as it was the title of one of his songs. The wife was in no doubt I was speaking to her husband. I wish I could write the phrase here, as you would be able to see how very unlikely it was that anybody would think of it, but it would be outing.
Of course, a sceptic could come along and say I had somehow researched the sitter and found out about her husband, his death, his music etc, but both she and I knew full well I hadn't. Actually, when I tried to research them online later on, I found I couldn't link her and him because his stage name was different to their married name.