The results you got with the flat battery on each current input jack look completely normal to me.
If the Fluke had a separate micro-amp function, which it does not, then the selector switch would be involved.
In this case, the amp and milli-amp jacks are always connected to their shunt resistors, a few ohms for the milli-amps, and "point something" for the 10 amp function.
This also explains why the current values were different.