This is left entirely up to the viewers's interpretation (as pointed out by KSmarts in comments).
The most that can be proven with physical evidence is that the machine definitely dilated time at it's core, as the static recording proved. Since no other evidence arose that ever showed the pod disappearing, other than the briefest of half-seconds as the rings obscured it, if you rely only on verifiable proof that's all you can take away. Even the damage to the chair inside the pod can be attributed to just the space-time dilation. Ellie admits as much, that it's possible nothing happened, in the hearing.
If you allow that Ellie's memory is accurate, it is highly likely she traveled. The details she picked up along her journey are not flights of fancy that she has had before. A completely contained metallic pod becoming translucent isn't something she's likely to invent. Nor in all her history has she had the kind of emotional response as she did at simply seeing the beauty in space that she did (allowing for that she was a very driven individual, and thus was open to it).
In addition, nothing eliminates both scenarios. The mechanics of the pod becoming translucent aren't really applied to any known science, just the potential of wormhole travel, and it's assumed in movie that it's just a container. It is entirely possible that the only thing that made the trip was Ellie's mind, the pod acting as a conductor or mental conduit, supplying all the images she witnessed. Through the wormhole connection, this could allow the other race to access her mind, and arrange a scenario that would allow them to communicate. Even if you don't buy that scenario, the aliens accessing her memories implies they could do pretty much what they wanted with them, and all of it could be retroactively implanted to say... well, whatever they wanted Ellie to get across to the rest of humanity.
The most obvious debate the movie has in itself is the pressure between evidence-based science and emotional-based faith. It intentionally never answers that question, to its characters or to its viewers. So as stated, it's up to you.