There are dozens of events of this type organised by Hackney primary schools week in, week out
Are there? Are you sure you're not confusing charitable donations with sponsorship? Are there really loads of events every week that get as much publicity as this one?
Sponsorship comes out of a company's marketing budget, therefore they usually expect to get something in return (normally exposure to an audience). The Jumble Trail is unlike any event my own DC's schools have ever done, as it gets way more publicity - eg it appears in local listings, in Time Out, it has a good online presence and it involves the local community, not just the parents at the school. Also, the local area was covered in professionally designed posters. I haven't paid a lot of attention to it but I wouldn't be surprised if there was a write up in the local paper.
All of these things are an opportunity to mention sponsors.
MN haven't (I presume) based their support of this school based on an altruistic desire to be nice to them (if they did, then the money would have come out of their charities fund, if they even give money to charity).
If a company sponsors something, then the marketing person making the decision about it will weigh up what they get in return for their money - eg how many people - and who - will see their name in association with this event.
I'm sure MN is really pleased to be able to support a school in this way, but it doesn't mean they have chosen this school over others for any reason other than they had the budget, it fits with their brand image and they get good exposure as a result so it's worthwhile doing. Probably the person selling sponsorship approached the. It's no different to mumsnet placing an ad somewhere, except that the money goes to a school (yay!) not a commercial company.
If you're planning something at your school, and it's going to get lots of coverage, why not ask MN to sponsor it? But don't expect them to do it as a favour, they'll do it if it makes sense for them to do so and they have budget available.
(If you're wondering why I'm so invested. I used to sell sponsorship for an event for a NFP. It's a common misconception that sponsors are giving money, as if to charity. But they want something back for their money, it's definitely not charity!)