I've never heard of milk "turning to water"?? I would be very skeptical of that. Did they actually have something officially diagnosed? The ony possibility I can think of would be that they have a horomonal problem. But that would be something that would have to be diagnosed by an endocrinologist after have their milk tested and bloodwork done.
It is much more likely they just were misinformed and didn't know what was happening. They probably had problems with BFing (normal problems) and got bad advice from a doc or mw.
The same thing actually happened to my sister. With her first, she had normal pain from BFing but it was really hard on her. 3 weeks into it her DD hit a growth spurt (normal time) and started feeding loads. A doctor told her she wasn't making enough milk, was starving her baby, and told her to go to FF.
Knowing what I know now, the doctor was completely WRONG! But I have never told my sister that because it would break her heart to know that she got bad medical advice and stopped BFing as a result.
With my sis' second DD, she BFed until 6 weeks -- then went on the pill as BC. She swears that the pill dried her up overnight, but I think that is highly unlikely. Again, I think she went through normal changes (your supply regulates then) and got bad medical advice. Again, I would never argue with her over it because it is in the past and I don't want her to feel guilty for her decisions.
So, bad medical advice when it comes to BFing is very common.
I suspect your mom had "normal" problems, asked someone about them, and got bad advice. Then, when your sister encourted the same situation, your mom said, "Well, my milk turned to water and I bet that is what yours did, too" and that was that.
I wonder if they hit the 3 week growth spurt. It is normal for babies to feed like crazy during that time and still never seem satisfied. It lasts for a few days (usually 3-5). Most moms freak out they are having supply problems and are very confused by it the first time. It would be very easy for someone to say, "Well, your milk is not enough for them anymore" and a mom to give up thinking they weren't making enough or proper milk. Which is totally wrong.
There is NO REASON to believe you won't be able to BFed your baby. You just need to know what you are in for. Lurk around the BFing section and read about the experiences of new moms and how they go about solving them.
If you have any other specific questions, feel free to ask! But I feel pretty confident that your milk will be just fine and you could BFed your new baby.