Michael raised a good point about if there is a difference between training to gain the full arts or if you are training to "patch a hole" in your perceived skillset.
To me this is clearly a continuum, when I trained in BJJ I had no intention of making it a long-term endeavor. I was training to get a clue on the ground, to be able to get good enough to reverse poor positions against decent wrestlers, and to be able to stuff most shoots. I got the first two, never got to the third. But that was my target going in, I never thought I was going to be a black belt or compete for a world title. I would definately consider this "cross training."
When I decided to do Kali, I think my approach was different, or at least my target was to get at a higher targeted skill level, eventually it became a true second art, but I am not sure when me doing Kali (two months, two years, etc) became not cross-training and truley pursuing a second art.
Anyway good topic for discussion, I am curious about other people's impressions.