Here is what I think it really, really important about the timeline update:
1. Why did the dog walker choose to tie Willow up with string, and not the lead and/or harness that was on the floor? It seems far more obvious to me to use the lead, unless the person was prescient enough to realise that it was a serious enough situation that it was important not to touch the lead or harness but to leave it in situ. BUT: I think it is incongruous to both think "I shouldn't touch the lead/harness", at the same time as "I had better get off to my appointment". It seems really inconsistent to me.
2. It has to be assumed that the dog walker had string on them, because it wouldn't be normal to go home to collect string, and hope/expect the dog to be where you left it, untied, some time later. Why did they have string on them? Maybe it's totally normal, but I still think important.
3. The dog walker returns home to inform family member, and the way it is described is that the family member arrived on the scene at 10.50, and called the school immediately. Why on earth does it take 1hr20mins for this family member to arrive on scene? Sure, it could be that neither was worried at all ('OK yeah, maybe I'll check that out, no rush') - in which case, why the string (just use the lead and harness!?)
4. In the time between 9.20 and 10.50 (1hr20 mins), are we really saying that nobody else passed the bench and didn't think it peculiar to see a dog tied to the bench with string, a phone on the bench, and a harness on the floor? If so, it's an absolutely vast time gap, and literally, anything could have happened.