Implication of finite choice from the BV discontinuity principle

Ascertain whether the finite choice principle for sequences of non-empty finite subsets of [0,1] (FCC: for any sequence (X_n) of non-empty finite sets in [0,1], there exists a choice sequence (x_n) with x_n ∈ X_n for all n) is derivable from the principle that for every function f: [0,1] → ℝ of bounded variation with infinite set of points of discontinuity D_f, there exists a sequence of distinct points of discontinuity of f.

Background

In Section 5.2 the authors examine reverse-mathematical strength of statements about bounded variation (BV) functions. They show several implication chains involving principles such as the existence of sequences listing discontinuities and various choice principles.

Immediately before the corollary, they raise a conjecture about the non-derivability of the finite choice principle from a BV statement asserting the existence of a sequence of distinct discontinuities when D_f is infinite.

This question probes the exact strength of discontinuity-listing principles in BV compared to finite choice over [0,1], refining the landscape of hyperarithmetical analysis developed in the paper.