Not true. When you actually 'train' in flats, moreso than just tempo runs/intervals/races/etc., you adapt your mechanics to the shoe. This means a lighter and more economical step, to the point where there's less wear with subsequent pairs. Thus, at first your mechanics may be sloppy and you can only get the suggested 250 miles out of a pair, but as you develop better 'control' with a lighter step, you could potentially get 1000+ miles out of a pair.
In Lore of Running (3rd edition, pg. 492), with regards to the studies by Cook et al. (1985a, 1985b), it states, "The authors also noted that the greater the original cushioning of the shoe, the more rapid the deterioration in cushioning. Thus, a shoe initially selected for its ability to absorb shock might prove to be inappropriate in the long term."
Grubinski is right, not just from an anecdotal standpoint, but it's supported by peer-reviewed research. If you have evidence suggesting otherwise, please share.
To the OP, this is something that requires a tremendous amount of patience, easy running, and listening to your body. With track season around the corner, it's tempting to suggest that you wait until the summer to transition. However, you could find a lightweight trainer you like right now and wear it once or twice a week on easy runs. If you feel good, progressively wear them a little more. If any real aches or pains pop up, make a change/do a bit of barefoot running (if possible)/go back to your regular trainers.