I think people are using the term gulfstream colloquially and some people may get the mistaken impression that the boost given to a storm may have something to do with the current. The boost comes from warm water which may not specifically be part of the gulfstream.

Someone should let Mr. Stewart know that:

A combination of Isaias moving over the warm Gulfstream waters during the convective maximum period and increasing frictional convergence due to land interaction with Florida should lead to an increase in deep convection near and over the center, as shown by simulated satellite imagery from the ECMWF model.