Unique magic triplets

Ruby, 46 51 58 bytes

->l{l.permutation(3).select{|a,b,c|a+b==c}.map(&:sort)|[]}

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Ok, not so straightforward, but now seems to work.

05AB1E, 11 10 9 10 bytes

{æ3ùêʒxsOå

+1 byte as bugfix for test cases like [1,0,-1] → [[-1,0,1]] (-1+1=0) and [-1,-2,-3] → [[-3,-2,-1]] (-1+-2=-3).

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Explanation:

{           # Sort the (implicit) input-list from lowest to highest value
 æ          # Take the powerset of this sorted list
  3ù        # Only keep inner lists of length 3
    ê       # (Sort and) uniquify this entire list of triplets
     ʒ      # Filter this list of (individually sorted) triplets by:
      x     #  Double each value in the triplet (without popping the triplet itself)
       s    #  Swap to get the original triplet
        O   #  Take the sum of this triplet
         å  #  And check whether this value is in the doubled list
            # (after which the filtered list is output implicitly as result)

The last four bytes could alternatively be œÆ0å (given by @Grimy): Try it online or verify all test cases.

      œ     #  Get all possible permutations of the triplet
       Æ    #  Reduce each by subtracting: [a,b,c] → a-b-c
        0å  #  And check if there are any 0s among the reduced permutations 

Jelly, 10 bytes

Ṣœc3ḤiSƊƇQ

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Ṣ             Sort the input,
 œc3          find all length-3 subsequences,
        Ƈ     filter to only the sets for which
      S       the sum of all three elements
     i        is an element of
    Ḥ  Ɗ      the set with all elements doubled,
         Q    and uniquify.