There is a relationship between surround stiffness and bass response, but it's not quite as intuitive as that.
A softer surround will lower the resonance, raise the effective volume (Vas) and lower the Q (resonant peaking factor) of the driver. In general, this results in a "better damped" bass (smoother, better defined, in general), that sometimes will extend to a lower rolloff frequency.
OTOH, a stiffer surround will do the OPPOSITE- raised resonance, lowered Vas, raised Q. This will result in a less-damped bass response... which some people find to be "punchier" (more "impact" in some cases). Sometimes, the stiff surrounds will result in a LOSS of low bass extension, in exchange for additional midbass output (ie, "punch").
The problem with the term "tight bass", is that it seems to mean different things to different people. To me, it's about clean, artifact-free response... but to others, it could mean very "fast", very "high-impact" response", possibly at the expense of ultimate resolution...
So, the answer to the above, is "it depends on what you mean by "tight"...
Regards,
Gordon.