Don't read too much into the MAPQ scores. These do not represent accurate measures and are more of "guesstimates."
Aligner developers apply certain heuristics using data estimates how often the alignment is correct, but the actual alignment correctness depends on the sequence and some sequences will never be reported incorrectly, hence the entire probability model is wrong.
A few MAPQ scores may have special meaning for example MAPQ=0 means multiply mapped read.
Note how the MAPQ=0 is actually wrong in that case, the chance of reporting the alignment incorrectly is NOT actually zero but depends on how many other equal positions are there.