NHC did in fact perform an operational assessment as to whether Barbara entered the Gulf of Mexico as tropical storm and said no. That said, I'm not one to always agree with the NHC but I too looked at satellite imagery when they made this declaration and I can find no evidence at any level there was enough of Barbara left for them to classify 91L as "Barbara". What remnants of Barbara, you bet; but generally NHC won't designate remnants that regenerate from the Pacific to Atlantic and vice versa the same name. In the same basin, yes!