New Java versions generally change both the Java Language (source and class file format) and the Java API.
The Java compiler can emit class files in the old format, even if the source is in a new format (these versions are specified by -target and -source, respectively). Therefore, you don't need the old compiler to target an old JVM.
However, the changes to the Java API are somewhat harder to account for. The easiest is to compile using the API of the Java version you target (-bootclasspath). Of course, you may feel confident that you are not using newer APIs, and skip this step, but the only way to make sure is actually compiling against, and testing on, the old runtime library.
In short, while cross compilation is helpful in that the same source can be used with different Java versions, you should compile and test against the actual Java version you intend to use, which does require the old JRE (or JDK).
BTW, all of these settings are also available in Java IDEs. For instance, in eclipse, one would set the compliance level in the project's compiler settings, and add the appropriate "JRE System Library" to the project's "Build Path":

rt.jarexists in Java 8 too...it would live in the JRE subdirectory though.jdk1.7.0_79/jre/lib/rt.jar). However, I would interpret the Oracle docs (in particular the last paragraph on the page I mentioned), that I must not use a rt.jar from Java 7, if the application is supposed to run on Java 6.