Why would a salty damp road be slipperier than the same road just damp?
It turns out there's actually some rather interesting science behind friction in the presence of water and salt.  Various model systems demonstrate that salt solutions really are better lubricants than plain (distilled) water between rubber and other materials, and by enough to matter.
Unfortunately little if any work has been done on the friction between real rubber and real wet roads in the presence of salt.  But there has been some work on more idealised systems.  One of the clearest results is from Experiments on the Lubrication of Raw Natural Rubber E.L. Ong and A.D. Roberts J. nat. Rubb. Res,, 1(1), 41-50 (1986).  Table 5 (below) is particularly interesting. Betwen raw natural rubber and Perspex the coefficient of friction reduced from 4.1 when dry, to 2.6 when wet and 1.5 when wet with salt solution.  A similar trend was observed for rubber-on-rubber friction. In other words in this system, in salt water there's about 60% of the grip compared to clean water. Fom the caption, &quot;Stickslip motion tended to occur and maximum friction coefficients are quoted&quot; (my emphasis). It's not clear whether this is true for all cases or just the salt solutions referred to in the preceeding sentence.

My journal access doesn't extend to reference 3 from this paper, Rubber friction in aqueous solutions containing ions, T.P.Mortimer &amp; K.C.Ludema, Wear Volume 28, Issue 2, May 1974, Pages 197-206.  But the abstract of this latter paper states:

In the case of water lubrication of black rubber at slow speeds and
low pressures the lubricating ability of water is shown to be enhanced
by addition of electrolytes to the water. It is thought that negative
ions from the electrolytic solution collect on each sliding surface,
repel each other and prevent the close approach of two sliding
surfaces. Thus a thicker water film exists between the sliding
surfaces than if the ion layers did not exist. The thicker film
results in a reduced viscous drag force, lower than can be accounted
for by conventional hydrodynamics.

The ~40% reduction in friction from the table quoted above is enough to negate a reasonable safety margin when it comes to grip.  Applying this to my case I suspect an element of bad luck came into play too: That some tiny slip became unrecoverable because the overall friction was too lowThis would be especially the case as dynamic (sliding) friction is expected to be lower than rolling friction, thus extra grip is needed to recover a skid compared to avoiding it in the first place.
Further Reading:

Rubber Friction in Aqueous Solutions Containing Ions
Friction of rubber on ice in the presence of salt
DLVO and hydration forces between mica surfaces in Li+, Na+, K+, and Cs+ electrolyte solutions: A correlation of double-layer and hydration forces with surface cation exchange properties
Effect of aqueous cations on friction between rubber and glass