Is this true about Carlos? If so, I am deeply shocked.
Yes it is, according to Kate's account.
The PJ had presumably made him watch the dog videos and possibly waved the "DNA" evidence. At that point, he may well have believed that they had substantial evidence and - somewhat naively but possibly with the best of intentions - suggested she confess to a lesser crime. The carrot was a short sentence, Gerry and the twins could go home, etc. It may seem incredible that anyone could falsely confess to a crime, but the psychological pressure of the fear of being charged with murder, plus wanting to get the twins safely back home could make "confessing" to a lesser charge seem the lesser of two evils.
It was pure bluff and he fell for it.
I find it somewhat naive because the next issue would be "Where's the body?". And then, of course, as it would have been extremely unlikely that Kate could have hidden the body and not told Gerry about it - bang. Her "confession" would be used to implicate Gerry who would most certainly not have gone home with the twins.
On the one hand, trying to get a confession is what the police do... and slippery stairs weren't an option in this case. The option they went for was to get her lawyer on board to "advise" her.
In those circumstances, I don't find it surprising that she was wary of being stitched up. My understanding is that she was fuming that her lawyer appeared to have been taken in by whatever he'd been told or made to watch during that 2-hour recess, and was fuming at the realisation that the PJ's conviction of their involvement meant that they had stopped looking for Madeleine. As she refused to "confess" to a crime she hadn't committed, her lawyer advised her to remain silent.
In addition, many of the questions were leading and there was no guarantee that if she had answered them, that they wouldn't have been distorted if ever there was a trial.
Here is what I find to be an interesting talk on the subject (from a US perspective).
https://www.youtube.com/watch?v=6wXkI4t7nuc