"If you had to deal with the claimant as part of you job, what would you say to her ?"
I think I have answered this already but if you missed it I'll try and do it more clearly:
If she was entitled to a grant - "I'm sorry your house burned down, here's the money you are entitled to"
If she wasn't entitled to a grant - "I'm sorry your house burned down, unfortunately we are unable to award you any money however here are some charities/freecycling people who may help you" (pretty much like the OP did)
What I wouldn't do would be to come on to Mumsnet and tell everybody her story and invite people to condemn her as they've done here. Like Peachy says, we have no idea why she spent the money the way she did.
As for the idea that trusting people enough to spend money wisely is the same as just handing it out to anybody who asks that's ridiculous. And with regards to assertion that governments always spend money sensibly I say to you PFI (a billion pound off-balance sheet scandal that we will be paying for for decades) and direct you back up thread to Sir John Bourn and his £390k expense account. If he's doing it, he won't be the only one.