Seems pretty smart to me.
I would assume Walmart would vet drivers in some way. Basically, if they fuck up a delivery to your home you rate the deliverer and if that driver has a few negative ratings they discontinue using that person.
As for liability, Walmart has to price insurance into their current delivery system anyway. The only question is whether Joe Public is more likely to damage a box than a Fedex delivery person. Personally, I think it's a coin flip. If the deliverer knows he'll make an easy $20 delivering to, say, 5 house in an hour, he's probably not going to fuck that deal up.
This delivery model would seem to drastically cut down on packaging costs, fuel costs, drive time. You don't have to box anything if it's just going in somebody's trunk.
Even more interestingly, it opens up the option to eventually order things like produce, dairy, eggs and meat online, because it will deliver within an hour or two instead of days.
Online grocery shopping has never been that viable because it always relied on maintaining a fleet of vans/drivers and all the cost/headache that entails. If Walmart only has to pay for 10-15 minutes of inconvenience for the driver, suddenly it may make more sense.
Very interesting concept.