Step 1: Understanding the Concept:
William Bateson and Reginald Punnett distinguished coupling (cis) and repulsion (trans) linkage arrangements in double heterozygotes.
Step 2: Detailed Explanation:
1. Statement I is TRUE: In a dihybrid heterozygote, when both dominant alleles are linked on one homologous chromosome and both recessive alleles on the other ($AB / ab$), it is termed the cis-heterozygote (coupling phase).
2. Statement II is FALSE: When both dominant alleles are present on both homologues in homozygous condition ($AB / AB$), the individual is a double homozygote, not a heterozygote.
Step 3: Final Answer:
Hence, Statement I is correct but Statement II is false.