Summary: Given a sequence of Boolean functions \((f_n)_{n \geq 1}, f_n \colon \{ 0,1 \}^n \to \{ 0,1 \}\), and a sequence \((X^{(n)})_{n\geq 1}\) of continuous time \(p_n \)-biased random walks \(X^{(n)} = (X_t^{(n)})_{t \geq 0}\) on \(\{ 0,1 \}^n \), let \(C_n\) be the (random) number of times in \((0,1)\) at which the process \((f_n(X_t))_{t \geq 0}\) changes its value. In [J. Jonasson and J. E. Steif, Stochastic Processes Appl. 126, No. 10, 2956–2975 (2016; Zbl 1347.60111)], the authors conjectured that if \((f_n)_{n \geq 1}\) is non-degenerate, transitive and satisfies \(\lim_{n \to \infty} \mathbb{E}[C_n] = \infty \), then \((C_n)_{n \geq 1}\) is not tight. We give an explicit example of a sequence of Boolean functions which disproves this conjecture.