Is the multiplicative anomaly relevant ?

In a recent work, S. Dowker has shed doubt on a recipe used in computing the partition function for a matrix valued operator. This recipe, advocated by Benson, Bernstein and Dodelson, leads naturally to the so called multiplicative anomaly for the zeta-function regularized functional determinants. In this letter we present arguments in favour of the mentioned prescription, showing that it is the valid one in calculations involving the relativistic charged bosonic ideal gas in the framework of functional analysis.