In terms of just the knot polynomials, there's a simple explanation for what's going on that makes gl(1|1) $\mathfrak{gl}(1|1)$ seem totally in place:
The knot polynomial attached to the defining representation of gl(m|n) $\mathfrak{gl}(m|n)$ only depends on m-n (the dimension of that representation in the categorical sense); you just get the specialization of HOMFLY at t=qm-n. $t=q^{m-n}$.
Furthermore, nothing much interesting happens at negative values, since they're basically the same as positive ones. So, our current techniques, which work for gl(n) $\mathfrak{gl}(n)$ knot homology, can't get at dimension 0, which can be minimally described as gl(1|1). $\mathfrak{gl}(1|1)$.
