To my mind, this is a matter of sales-semantics. "Mid-sized SUV"/"Crossover SUV", to me, is marketing-speak for "nobody in the US wants to admit to driving a stationwagon". Crossovers are "estate wagons", which would place Fisker just fine in the EU. It's the full-sized SUVs, like the Suburban, which had trouble selling in Europe.
You raise an excellent point which we have had to manage in our work. SUV had a historical definition which included body-on-frame architecture, selectable 4WD, and similar attributes. Over time, this has been watered down and confounded by the more recent use of CUV/Crossover. That term was launched by the industry to acknowledge vehicles that were "crossing over" from being an SUV to actually being a variation of a passenger car. Over more time, both terms have been used interchangeably and both have lost clear meaning. At our company in this industry, we simply use UV for all utility vehicles, and even that has its' weaknesses as we recognize that many so-called UVs are just tall cars on unibody architecture with RWD or full time AWD....not quite the historic Wrangler, Scout, or Bronco of decades ago.
We did some consumer research with silhouettes. First, please understand my use of 2-box vs 3-box. The "box" is a portion of the car....hood/passenger compartment/trunk. A conventional sedan is a 3-box design. A UV is 2-box, with no protruding trunk at the rear. The research showed us the level at which most respondents think:
Silhouettes shown and consumer category:
3-box usual height = car (2 or 4 door)
2-box usual height and long length = station wagon
2-box usual height = hatchback car
2-box tall height = SUV
It seems "SUV" has taken most share of mind, perhaps some also have heard or use "Crossover", but these are judged on the taller height and shape. But, the true meaning of SUV is long gone and now most people simply think of it as a shape, not a function, based on the research we did.