The null hypothesis of Kruskal-Wallis test and Wilcoxon rank sum test is the mean ranks of two groups are the same, not the medians of two groups are equal. When the distributions of two samples are different, even they have equal median or mean, the two tests can still reject the null hypothesis, and conclude the two distributions are significantly different. So if you want to compare medians, the quantile regression or the CI of medians can be used as the link described given by @Rick_SAS.
Sorry I don't know much about Hodges-Lehmann CI of median, so cannot answer why the results from EXACT HL is different from the results of PROC QUANTREG.
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