Influencer wanted free cakes instead of paying for them herself and the bakery said no. Influencer throws babies out of the pram. Bakery gets free exposure and influencer looks like a prat.
No, according to your story, an agency wanted that not the "influencer" (who is actually apparently some soap actress rather than an "influencer").
It's pretty standard for people with a following to be paid for promotional stuff though usually, it's the other way around, advertisers/agencies etc.. approaching them rather than them trying to solicit stuff they want. There was another story with an "influencer" type rather than a celeb wanting a free stay in a hotel in Ireland.
Just the epitome of freeloaders wanting something for nothing.
That said I'm not sure why the bakery is publicising their response either? A polite no thanks, or even just no reply at all and no-one cares right?
Well they don't want something for nothing, they want something in return for some publicity, something that does have value.
As for why the bakery is publicising its response - publicity having value again, this story has now gone viral and they've got a load of positive attention. They've also thrown in the stock phrases about how exposure doesn't pay their bills etc... that might be the case with say actors and other artistic people working for free but if you're running a small business then advertising does tend to help bring in customers and pay your bills.
The initial e-mail seemed off as they made very vague comments and the promise of some coverage in OK magazine has since been undermined by the celeb saying they're not involved. I think any small business taking up such an offer ought to check who exactly it is for, what sort of numbers they get for their social media posts and give some strict requirements like there must be at least one post featuring the cake itself (and not in among a selection of photos on the same post) with the bakery named and tagged on the first line of the comments etc.. + [some requirements re: duration it must remain, story posts for the other items and cake photo, not posted at the same time as a bunch of other updates from the same account etc..etc..) and if not fulfilled then an invoice of £X is due etc..
It just seemed quite vague and like complete chancers but it could be worthwhile in theory (if the bakery does mail-order stuff/isn't just local), supposedly someone with her following should be able to get $1000 - $3000 per post and if that's enough to cover the two cakes + cupcakes then... maybe worth a shot.
Also, it's hilarious how the husband shares her birthday but is apparently only getting a smaller cake.