Step 1: Understanding the Concept:
Three-point genetic linkage mapping: physical proximity between linked loci increases positive chromosomal interference, making double crossover frequency extremely low, and detecting double crossovers strictly requires three heterozygous gene pairs.
Key Formula or Approach:
\[ \text{Expected DCO Frequency} = \text{Recombination Frequency } (R_{12}) \times \text{Recombination Frequency } (R_{23}) \ll 1 \]
Step 2: Detailed Explanation:
1. Statement I: When three linked genes are positioned close together on a chromosome, the individual single recombination distances ($R_{12}$ and $R_{23}$) are small; their product (the expected double crossover frequency $\text{DCO} = R_{12} \times R_{23}$) is extremely low (often approaching zero due to positive chromosome interference where one chiasma physically inhibits adjacent crossovers). Claiming it is 'very high' is false. Hence, Statement I is incorrect.
2. Statement II: To detect and map double crossovers (double exchanges), a three-point testcross investigating three heterozygous gene pairs ($A/a, B/b, C/c$) is mandatory (middle gene switches relative to flanking markers). Hence, Statement II is true.
Step 3: Final Answer:
Therefore, Statement I is incorrect but Statement II is true, matching option (D).