That means that in US English get has two past participles
I think with possesion and obligation, it kind of acts as if it were he present simple, eg I've got a pen. (having got it I now possess it.) I think it's really used because it's easier to say. Nevertheless, this is truly a strange construction.
I have added it to my Venn diagram, which is now getting a tad unweildy. I never knew verb patterns were so complicated. I have to get round to writing stuff in some of the new links now. Oh well, it's got to be done.