What is the resistance used? It might be having more of an effect then you think. If the manual I pulled up is the right one, they list the 8842 as only going upto 2A dc, and the burden voltage as "<1v" (annoying, just tell us what resistance shunt you use on that range...)
My agilent 34401 on my desk uses a 5 ohm resistor for the miliamp range, and a .4 ohm resistor for the 3A range, 1V burden for 2A would suggst a .5 ohm shunt for the 2A range on the fluke bench meter, which would have been ~.4v on high.
VS a typical handheld DMM with a 10A shunt ( ~.03 ohms on my fluke 73) , which actually makes it a better choice for current draw measurements. Evenmore so on direct drive LED lights where any voltage loss drops current by a lot.
PS: Did someone get a new benchtop DMM and is having fun playing with it? Or just bored at work? ;) Find something to use as a current source, and string the fluke and a handheld meter in series and check (or calibrate if you dare venture inside) the handheld meter :D