Following my answer to this question, a debate ensued on whether the loss in population of one species (namely red squirrels) due to its lesser resistance to a pathogen brought by a competing species (namely squirrel parapoxvirus and grey squirrel) should be labelled as a result of interspecies competition or not. Here I will try to state it as a question with in a more general setting. I'll give my own answer to it, and would welcome other views on the issue.
Assume the following: Species $A$ lives in a closed ecosytem and has reached carrying capacity $A=M_A$. At time $0$, a new species $B$ is introduced which is in competition with $A$, and additionally bears a pathogen to which it is resistant but which causes a high lethality rate in $A$.
It is observed that $A$ dimishes while $B$ thrives. Can we necessarily ascribe it to interspecific competition?