Yes, the Camerons did claim DLA for Ivan. I don't have a link to the interview where he said so, but I've seen it.
And yes it is a passporting benefit. Though I can't off the top of my head think of anything it passports to that the Camerons financially need. Eg Disabled Person's Railcard, exemption from household benefits cap... I suppose blue badge parking spaces closer to an entrance might be handy, but they don't need free parking.
BTW, I support DLA being non-income related, like many pensioner benefits. Apart from anything else, mobility DLA may enable someone to earn - you don't want a negative feedback loop there.