bedtools closest default?

Question

[vctrm67]

I'm confused about the default behavior of bedtools closest. I ran the command bedtools closest -a a.bed -b b.bed -k 1 > closest.bed and got this as a part of the output (the columns correspond to chrom, start in a.bed and chrom, start in b.bed):

9   5819608 9   5819608
9   5819608 9   6080573
9   5819608 9   6164857
9   5819608 9   6278938
9   5819608 9   6506183
9   5819608 9   6507818
9   5819608 9   6832603
9   5819608 9   6957619
9   5819608 9   7010222

However, the only region in a.bed this corresponds to is (the columns correspond to chrom, start, end):

9       5819608 8043573

and the only segments in b.bed that are relevant are (the columns correspond to chrom, start, end):

9   5086998 5326535
9   5326536 5819607
9   5819608 6080572
9   6080573 6164856
9   6164857 6278937
9   6278938 6506182
9   6506183 6507817
9   6507818 6832602
9   6832603 6957618
9   6957619 7010221
9   7010222 8043572

But it was my understanding that, for default behavior, bedtools closest only reports multiple regions in b.bed if there is a tie. However, I don't see a tie here; the only closest regions should be the first and last regions of the segments posted in b.bed, no?