It's of course (2). That's the "trick"! Instead of a weird esoteric interpretation of something "traveling backward in time", contradicting the causality postulate underlying all of physics you have a causal interpretation of the negative-frequency modes of free relativistic fields. The important point is that the trick works for quantum fields, and here it's mathematically extremely elegant:
(a) you look for the irreducible ray representations of the proper orthochronous Poincare group (in fact boiling down to the proper unitary representations of that group, because it has no non-trivial central charges)
(b) you assume locality/microcausality as well as stability (i.e., that the Hamiltonian is bounded from below and there is thus a ground state)
(c) this inevitably leads to the necessity to superimpose both positive- and negative-frequency modes in a specific way to get local quantum fields, realizing microcausality of local observables and local realizations of the Poincare group.
(d) Quantization implies that the operator-valued coefficients in the mode decomposition in front of positive (negative) frequency modes must interpreted as annihilation (creation) operators to have a causal interpretation.
(e) Taking all this together you end up with the profound very general properties of local relativistic QFT: physically interpretable are the representations with ##m^2>0## and ##m^2=0## (massive and massless particles; tachyons make trouble, at least whenever you try to make them interacting); the connection between spin and statistics: half-integer-spin fields have to quantized as fermions and integer-spin fields as bosons; the discrete operation CPT (charge conjugation, space reflection, time reversal) is necessarily a symmetry. All of these conclusions are experimentally confirmed at high accuracy (including the violation of P, T, CP, etc. symmetries by the weak interaction).
You find all this described in a very concise way in Weinberg, Quantum Theory of Fields, Vol. 1.
