Interesting posts, plibble and debby.
Plibble - you touch on an issue that needs explaining. Breastfeeding counsellors never give 'advice', or they shouldn't....that's not how it works. We explain options, and help a mother explore how she can achieve her aims, and we support her.
I have never 'advised' anyone to give (or not give) formula or water, though I have spoken to many women who have done so, or who want to talk about whether to do so.
Even on here, where you are not really in dialogue with women, I don't think I have ever 'advised' anyone - I might make suggestions on how people can tell if they are getting the right sort of help and I might suggest what they can do to resolve a situation but it's phrased (I hope) in a non-advice-giving way.
In your situation, where you say your baby was 'breastfeeding so much she was throwing up' I would explore that with you - was this normal possetting, maybe? Or if it wasn't, then this is not normal, and would need a medical opinion.
I don't know why the 'adviser' said you should drink more but she was almost certainly right about the baby not needing water. I don't think the odd drink of water will harm an otherwise healthy, thriving baby, though. The reason why it's not needed is that breastmilk is mostly water and anything other than breastmilk risks upsetting the supply-demand link.....as a one off it's not gonna do anything longer-term, however, so no real point in worrying either at the time or now!
You're right about situations being more complex than black-and-white solutions imply. That's what lies behind breastfeeding counselling - helping the mother find the approach and response that is right for her and her baby. If someone wants to give formula (or water) and feels that this is right for them (and sometimes when bf is going badly, there is a health case for giving formula at least in the short term), then a breastfeeding counsellor will help her work out a way of giving it that has the least impact on her choice to continue breastfeeding.