I found a way to brute-force it with the text function. The example below is for the percentiles only. I didn't try labeling outliers.
The variable i is used to call each dataset (I don't know how you organized your data) and also used to place the labels in the first, second, third, etc. columns. I nudge the label a bit (0.1) to right of center of each column, and a bit (5) above each line.
First you need to make your boxplot, and then:
point = quantile(Data,0.25); text(i+0.1,point+5,num2str(point,'%.0f'));
point = quantile(Data,0.50); text(i+0.1,point+5,num2str(point,'%.0f'));
point = quantile(Data,0.75); text(i+0.1,point+5,num2str(point,'%.0f'));
point = quantile(Data,0.75)+1.5*iqr(Data); text(i+0.1,point+5,num2str(point,'%.0f'));
point = quantile(Data,0.25)-1.5*iqr(Data); text(i+0.1,point+5,num2str(point,'%.0f'));
Good luck to others who stumble on this.