Well, I didn't use rope for starters and I am struggling with the notion that string couldn't be pulled through a closed window - I did it with my own last night.
I don't think you're struggling with it, just with convincing others who don't agree.
I accept that your method is possible, having once lived in an old house of similar age to WHF, and fitted with sliding-ash windows which rattled and were draughty during windy weather, until they were replaced with new casements. Over many years the wooden frame shrinks leaving gaps around the sliding portion, making them easier to open and shut. Security is easily overcome by sliding a thin object such as a hacksaw/thin knife blade between to open, or in your case a string to close the catch. Being in a toilet/shower room too would mean more use for ventilation than those in other rooms, hence more wear.
He might have had more of a problem replacing all those toiletries on the sill, then arranging/straightening the net curtain, than repositioning the plastic drying rack, liquid soap bottle, etc. in front of the opening casement kitchen window. Which is why I think the latter was the easier escape route of the two.
Either way he got out, leaving WHF secure and police flummoxed.