Symbols must behave under EQ as they traditionally always have if symbols are to be useful as property list indicators.
There is a semantic issue that is not explicit in the ANS but which underlie language semantics and the concepts of "same", "identical", and "equivalent". It concerns object mutability.
The only objects for which the EQ/EQL distinction is unspecified are characters and numbers. But hese objects are immutable (at least in the portable language). Most other kinds of objects, including symbols, are mutable. The fundamental principle of "identical" is that if two objects are EQ, mutating one of them [sic] will necessarily mutate the other. If two objects are _not_ EQ, then mutating one will _not_ mutate the other.
I would propose that since symbols have several mutable properties, mutating a property of one reference to a symbol will mutate that property of another reference iff those two references are EQ. The "only if" part of "iff" is here crucial. This is exactly the same as for conses, arrays, structure slots, hashtables, readtable dispatches, etc. etc. etc.
It still isn't clear whether this obvious semantic property can be proven from the ANS.