I've never measured current draw like that personally, I'm assuming that you are measuring the voltage drop across the resistor to determine current draw?
I've always just run the MM probes in series, but I guess at the current we are talking about that doesn't work well(my Fluke limit is 10a I think).
I'm assuming it's a grounding or Coupling issue in the Scope,. and it seems like the scope is actually acting as it is inline/parallel because of the resistor.
It's been a LONG time since I've used any of that side of my brain, I threw out all my books/electronic parts years ago when I determined that I didn't need to fix stuff anymore(IE: didn't build RF amps or anything anymore- it still took a LOT of effort to throw boxes of parts and books away after years of building stock) cuz most things these days are throwaway..I'm wondering if you need some kind of coupling circuit/cap to keep the Scope out of the line, except to measure across the resistor.