Do I need a compo face?

Hip-pop

This is pure deflection just like you see everywhere in modern life.

The op fails as a parent yet it's someone else's problem.

Hope your child recovers and doesn't have lasting injuries.

hip-hop?

Probably in the same way as a small number of kids garrote themselves with blind and curtain pull cords or otherwise kill themselves with innocuous domestic items or in the good old bad old days drown in stagnant water or suffocate in abandoned fridges; they're kids and they muck about, if there's something dangerous they'll gravitate toward it like bees to nectar or tiny imps of the perverse.

Not entirely sure, as I said we didn't have our eyes on him for a few seconds, but I presume he picked up a discarded cable tie from the floor and somehow managed to get it fastened through trial and error - juts bad luck it worked.

Very good

Just to raise a pedantic point - if each of those bullets has to be satisfied (i.e. it is an 'and' not an 'or') - and that's how it reads to me - then I'm not entirely convinced that the first bullet point is satisfied.

The OP's timeline is a little hazy (deliberately so?) as it really doesn't give any indication as to how much time passed between the staff member putting down the tea (in the space cleared for that purpose by the OP), the OP's wife getting distracted by putting the books away, the staff member leaving (assuming they did walk away?) and the child hooking the tea-pot and scalding themselves.

On a slight tangent for a second - wouldn't you usually consider waiting staff bringing something to your table somewhat of a 'transition'? They have a job to do, but so do you. Kids or not. If someone's bringing me my Sunday Roast, I'll be looking down at my part of the table to check their path is clear. If they're bringing a tray of drinks, you'd be ready to say "mine" when they call out your drink. That sort of thing. It is (or should be, in polite circles) an interaction. You don't take that opportunity to ignore the waiting staff, do your own thing, and make it entirely their responsibility. Do you?

Back to my point, though... Although there's probably no 'defining moment', there is a point at which the waitress' role in bringing the tea to the table was 'complete'. A point at which, even if she'd not quite put them in the optimal spot, the act of bringing them and putting them in front of the parents transferred total responsibility to them. Certainly in the absence of either parent giving explicit instructions as to where the tea should be placed, or taking the opportunity to say 'No, not there you effing idiot!" when she placed them (not unreasonably) in the middle of the table, there's a strong sense in my mind that the waitress' role was 'complete', Especially if she'd then moved away and more time had elapsed.

In other words, if the OP or his wife didn't take any care to give the waitress specific direction; didn't take any responsibility for providing guidance or explicitly disagree with the waitress' choice of position, and she sets down the tea and walks off, what may or may not happen next is 100% the parents' responsibility.

Fact is, the OP saw the waitress coming and made an unconscious (or possibly conscious) decision to not interact with her, and to focus on his son instead. He didn't check to see if his wife was taking charge, or able to interact with the waitress. They both left 100% of the decision-making to her purely by deciding not to be helpful, or be part of that 'transition' process that happens when someone brings you something.

It is no wonder they blame her in hindsight.

For me, the primary issue isn't that they blame the waitress - it is that they couldn't even be bothered to help her complete her task in the first place. Absenting yourself from that interaction usually only has rudeness as a consequence - but this time it was so much worse. I feel sorry for the girl and hope she recovers.

OP - as a human being, if you chose to silently pass all responsibility to the waitress without any other communication, aside from moving a few books around, then shame on you. That's not how to interact with someone who is bringing you something.

Back to my point about the first bullet. If the waitress has put the tea down and has gone, it is no longer a 'work activity'. The tea is now the responsibility of the parents, who are not paying proper attention to what is going on around them.

The OP was an awful read and it took a massive nose dive when the 10k got mentioned.
Staggered that he thought airing this in public would be well received.

There are two types of parent in this situation ;

1) The ones who feel extremely guilty for not taking proper care of their child, they feel terrible about it but learn from the experience and focus their attention on their child. It wouldn't even enter their thought process to start blaming other people. In fact, they'd probably look to thank the 5 staff members who very kindly assisted.

2)

Depressing thread, but sadly not surprising.

Yes, but the tray was placed in the middle of the table, as is normal for communal stuff, for patrons to then deal with themselves. If the server starts placing it offset then the dopey parents will knock it over while faffing about with their books and be here whining how the server was negligent, placing it near an edge, how they could see the parent was moving about and how do they get their compensayshun.