In a fine poem, "meaning" is a nebulous thing. One could always take John Ciardi's tack and ask a more fruitful question: How does a poem mean? Then the emphasis becomes one of appreciation -- for the craft of the work, the form, imagery, the economy, the flow, the diction, the tone, the word choices, etc.
The fact that poems don't easily convey clear-cut meaning is the reason why newcomers to poetry often find it bewildering. "But what does it mean, what does it mean" the student begs to know. A nice way to get them thinking differently is to have them compare a poem such as "If" which states its meaning outright -- these are the things that make you a man, my son! -- and something more subtle like "The Road Less Travelled."
However, let me look at the opposing statements again.
A poem means whatever a reader perceives it to mean. All readers' interpetations are equally valid." Well, "interpretation" is a nice word and not necessarily hinged to clear-cut meaning. I daresay that The Road Less Travelled [Late edit: I meant Stopping by Woods, of course, as noted by Golias, below; brain death imminent!]invites different interpretations, some that would concentrate on the speaker's worldly obligations, others that would read more of a "world weariness" into the phrase "miles to go." The woods could be interpreted as a temptation to shun one set of responsibilites for another, or as the unconscious, or as death. Many interpretations are valid but not all. No doubt the teachers among us have listened to many a harebrained interpretation.
A poem means what its author intended it to mean. The best interpretations come closest to that. That's probably true, isn't it? A fine chef selects prime ingredients, prepares them artfully, blends flavors surprisingly and invents a savory new dish. If it's a complex cassoulet then it's not a cheesecake. We access the bubbling unconscious as we write but we also make choices as we write (and rewrite and rewrite). We know what we've wrought and if we've done our job well, careful readers will get the idea. Still, "meaning" in this context is still a nebulous thing! Or elastic, anyway.
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