Your apparent paradox is NOT related to the parameterization (the "other" factor is at its expected value, not 0, but this is not the point anyway). The global test is not just concerned with pairwise contrasts, but all possible contrasts. With 4 levels to a factor, there are all kinds of factors, such as 1 vs. the mean of 2, 3,4; 1&2 vs 3&4, etc., etc. You will not necessarily find the reason for the global significance by looking a sample of the possible contrasts. Also note, all test results can be wrong. You can get false positive or a false negative on any test.
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