Rust hole on tube between chain stays
When building frames high quality tubing, such as Reynolds 531 is often only used on the main tubes (i.e., main triangle) and if you are lucky the rear triangle.  Less critical tubes, such as the cross-brace, will typically use a lower quality steel, such as a mild steel, which is more susceptible to rusting and will show earlier signs of deterioration. Therefore, there is still a chance that while the cross-brace has severely deteriorated,  the main structural frame may have remained relatively intact. 

There is of course no way to know for certain until you strip off all the components and paint and really have a close inspection of the main structural tubes.  Once the paint is off you can can see how deep the surface rust goes. You can also try tapping the tubes lightly with a small hammer to see if you hear tone changes (i.e., severe thinning due to interior rusting). Careful inspect the chain and seat stays as some frame builders use cheaper steel here, which may not have faired as well. Finally, the cross-brace was often used for fender mounting and was usually drilled, paint damage at this point is also common which could have further accelerated the rusting.

Even if you do all this and the main frame seems reasonable intact, I would still be cautious in use as there is no way to determine with absolute certainty the safety of the frame without pressure testing it (i.e., ridding it). This is a delicate proposition as you want to ride it as lightly as possible until you see how it reacts and slowly build more confidence as you use it in differing situations. One of the things working in your favor is the failure mode of steel is a lot better than other frame materials such as aluminum and especially carbon, which you should generally avoid riding if you have concerns over structural damage.