This is not true. It's a common misconception.
The hair strand is continuous, and though hair is dead, it has layers that are continuous and feed right from the bulb. What you give to your body is not only apparent in the new growth, it is also spread throughout the core of the hair- (again because the entire strand is one continous length and it feeds out from the bulb). Since there is no disconnect between the bulb and the rest of the hair, what is available to the hair at the root, will eventually spread out to the tips/ends of the strand. You may notice it first at the new growth, but it will also make a difference in the hair that has already grown out (though this may take longer).
You can see between the root (bulb and papilla) and the rest of the strand, there is no division or block to the spread of nutrients and minerals to the rest of the shaft. This is one of the main reasons doctor can take tell whether you have ingested certain drugs by studying your hair strands (whether the roots are in tact or not!)
Oh yeah PS- I'm in too!