edit: woops i took too long and half of what i said was said during the writing of my post. sorry.
i'll start off with something useful. if ever someone makes a fedex faq this should be #2. #1 should be require DIRECT signature, or else send it to be held at a fedex / fedex kinko's location.
my useful tip: to skip talking to machines, press 0 on the keypad when it starts asking you to talk. twice is basically a guarantee you'll get a person.
Kendro is correct on the signature part. Residential signature is an option that the sender must choose, and there is an additional fee. You can choose between No signature, Direct signature, and Indirect signature. If you don't choose anything, it defaults to no signature. It used to be the other way around. You used to have to specifically state that you didn't require a signature, but it hasn't bene that way for some time now.
I don't know the official reason it changed, but i assume it is because of the number of complaints that "well i can't be home for that and i don't want to have to drive to a fedex office to get it"
it possibly had something to do with the increase in gas costs, and the subsequent increase in delivery costs if they had to keep attempting to redeliver to get a signature without the customer actually requiring it.
As far as fedex's liability, that also depends on how it was sent. if this guy is cheap enough that he didn't require a signature, then he likely didn't declare the value of the item inside the box, as for every $100 over $100 there's an approximate $1.20 fee. (ie if you declared $100 or less there is no fee, if you declare $101 - $200 there is a ~$1.20 fee, $201 - $300 ~$2.40 fee, etc)
So for a 360 he would have had to pay an additional $3.60 for a 400 dollar declared value, and $2.50 for signature. It would have added $6.10 to to shipping cost, and that is obviously way too much to have to pay to ensure the safety of your 360.
Fun additional note: had he just lump summed the value to $500 he would have gotten the Direct Signature "forced" upon him, as fedex requires direct signature for declared values of 500 or more. Which means he could have gotten the value and signature for $4.80. They would have made him let them inspect the package, but you'd almost want that, as that means someone other than him could confirm that the 360 was in good (physical, at least) condition when it began the shipping trip, and had anything happened to you would have had recourse.