Weak point: Concentration in the slime is very low, and this alone should be the driving force for mass transfer. Binding can't help unless the binding agent is positioned better along the route of mass transfer, e.g., on the surface of the slime. This is far-fetched because no organisms should expend its resources making the slime better for all the others. Conclusion: No active transport explanation.
Further reflections: If the transport is by passive diffusion, the concentration in the slime approaches the concentration in the bulk asmyptotically. An organism in the bulk has the advantage. This leads to the conclusion that attachment is solely for the purpose of keeping the organism in the system. Those in the bulk go elsewhere to survive or die