TL;DR It depends on the vegetable, and what other preparation method you're comparing it to.
A study in the Nov 2003 issue of Journal of the Science of Food and Agriculture (Paywall--some key points explained here). From the abstract:
High-pressure boiling, low-pressure boiling (conventional), steaming and microwaving were the four domestic cooking processes used in this work. ... The results showed large differences among the four treatments in their influence on flavonoid and hydroxycinnamoyl derivative contents in broccoli. Clear disadvantages were detected when broccoli was microwaved, namely high losses of flavonoids (97%), sinapic acid derivatives (74%) and caffeoyl-quinic acid derivatives (87%). Conventional boiling led to a significant loss of flavonoids (66%) from fresh raw broccoli, while high-pressure boiling caused considerable leaching (47%) of caffeoyl-quinic acid derivatives into the cooking water. On the other hand, steaming had minimal effects, in terms of loss, on both flavonoid and hydroxycinnamoyl derivative contents. Therefore we can conclude that a greater quantity of phenolic compounds will be provided by consumption of steamed broccoli as compared with broccoli prepared by other cooking processes.
Now whether the nutrients studied here constitute "important vitamins" is an exercise left to the reader.
According to another study from the Journal of Food Science (paywall), summarized here:
Results showed that, depending on the vegetable, cooking on a flat metal surface with no oil (griddling) and microwave cooking maintained the highest antioxidant levels.
Note that these studies are not limited to the "washing away" or leeching effect on nutrients, but also consider the destruction of nutrients during cooking. The latter obviously does not directly answer your claim, but is probably equally relevant to anyone interested in food nutrition.
In summary, the preferred cooking method likely depends on your vegetable, but boiling is known to leech nutrients (sometimes this is even beneficial, as in the case of Swiss chard, where boiling allegedly reduces the acidic content [source]). I've also seen (unreferenced) claims that Spinach ought to be boiled briefly, or blanched, to help release vitamins.