After looking at it for a bit I've determined that it's not so much a problem that you can't pick a unique LCA (you just need a guarantee that either works). However you run into problems when you merge two nodes that already contain some merges. Consider the following example:

        0
        /\
    +1 /  \  +2
      /    \
     1      2
     | \  / |
     |  \/  |
     |  /\  |
     | /  \ |
     3      3
     | \  / |
     |  \/  |
     |  /\  |
     | /  \ |
     ?      ?

Here you've got two choices for LCA (which aren't equivalent but that aside), both will give you the wrong answer. As the correct answer should obviously be 3 as only 1 and 2 were ever added to the counter, exactly once.

Basically the problem is that the merge operation isn't idempotent, hence it doesn't define a semilattice, which seems to be what you want if you want to ensure consistency even over distributed systems.

They could have easily fixed this by picking a better merge operation such as a union or maximum, but it's not encouraging when someone picks an illustrative example that doesn't quite work.