Conditional independence is a hard concept and you may find Ch07.06 Part (c) iii on the McIsaac Score and the Rapid Antigen Detection Test confusing. Attached to this post and added to the syllabus is an optional expanded version of Ch07.06 that walks you through a numerical example of how independence of two tests conditional on D+/D- does not imply that the two tests are unconditionally independent. If you work this optional expanded version of Ch07.06, you should turn it in with PSet 6. You are more likely to get the required question Ch07.06 (c) iii correct, and you may understand better why conditional independence does not imply unconditional independence. For those who don't do the optional expanded version, here is the best I can do in the absence of a numerical example.
Assume Test A and Test B are both dichotomous. Take all the patients who are negative on Test A. A few are D+ (false negatives) and many are D- (true negatives). Now, in these patients who are negative on Test A, measure the sensitivity and specificity of Test B. Sensitivity is measured in D+ patients who were negative on Test A. Specificity is measured in D- patients who were negative on Test A.
Separately, take all the patients who are positive on Test A. Some will be D+ (true positives) and some will be D- (false positives). Now, in these patients who are positive on Test A, measure the sensitivity and specificity of Test B. Sensitivity is measured in D+ patients who were positive on Test A. Specificity is measured in D- patients who were positive on Test A.
If (Sensitivity when test A is negative) = (Sensitivity when test A is positive) and (Specificity when test A is negative) = (Specificity when test A is positive), then the two tests are conditionally independent; you can multiply their LRs. However, if you don't condition on D+/D-, a positive Test A increases P(D+), which makes a positive Test B more likely.