Sounds like to me. I have liability on my truck and Jeep and full coverage on the other Jeep and Civic. Find out if that is something unique to your poiicy only (make them show it to you in writing). Sounds like they are trying to get out of something.
Not sure what your trying to say about splitting coverage, but read over our policy carefully, They often will make an initial verbal denial of coverage hoping to weasel out with not accountability. When i crashed my MC hitting a Deer last August, they initially stated I had no injury coverage, when in fact I had $15k. Coverage is a per vehicle deal (each car and its coverage is specifically defined.) , unless you have fleet coverage. But most folks dont have that.