As I said, I don't think the stones are the oil, so it doesn't matter if you throw it up. I too have vomited and got coagulated bile.
The oil causes alot of bile to be expelled from the liver, there is no doubt about that. It is because of the sheer force of this release that these globs are formed.
When people do not get stones the gallbladder and liver must be feeling particularly sluggish for whatever reason. This is probably the reason why we have symptoms in the first place- the inconsistency and unreliable nature of bile release from the liver.