Henry........I beg to differ on what the paint companies offer. Paint companies make a huge range of product primers - and they are not just watered down paint. Specialty manufacturers like Zinsser make some great products - you can't beat B-I-N for stains.
However - what I think what Sarah has here is a basic PVA Drywall primer. Even very good ones aren't the best for a wall that is obviously impregnated with W/C Glue. It sounds to me like that is the issue here - I have seen that before - people think they have removed all the glue - they haven't - and when the chemicals in the paint hit it - a sticky gooey mess happens.
I would recommend B-I-N in this instance - or perhaps a Glidden product called Stain Jammer.