No, the greater tensile strength of basalt fiber versus glass fiber is due to it being partly crystallized, similarly to the greater strength of glass-ceramic vessels (i.e. which are made from a glass for easier formability, but then they are crystallized by a heat treatment) versus glass vessels.

While there are glasses much stronger than ordinary glass, there are a lot of even stronger ceramics, which are (poly-)crystalline.

Glasses have many advantages vs. other materials, e.g. easy processing for making any shapes, including fibers, no porosity, chemical resistance, optical transparency and so on, but strength is not one of them.

The glass content of the basalt fibers is useful for allowing them to be drawn into fibers, by being soft enough for this even at a temperature under the melting point of the basalt.