Cross-over effects in strength training: Strength train a single leg. That leg will get stronger, and to a lesser extent, the other leg will increase in strength as well. Strength train just the quadriceps. The quads get stronger, and to a lesser extent, the hamstrings do too.
The same occurs in stretching; stretching a muscle of one leg has a "cross-over effect" that produces an increase in flexibility of the opposite leg. It is thought to be a localized change; one leg affects the other.
Will upper-body stretches affect the lower body? From this study, Acute bouts of upper and lower body static and dynamic stretching increase non-local joint range of motion:
“There were significant shoulder range of motion (ROM) increases following lower body stretches. There was a significant hip flexor ROM increase following upper body stretches.
“Rather than a mechanical or neural drive mechanism, an enhanced stretch tolerance was likely the significant factor in the improved ROM”.