It's true, but only for AC. DC frequency is 0Hz so it doesn't apply. As frequency gets higher, the more that the current will travel at the outside of the conductor. Which is why microwaves (very high F) use waveguides, which are essentially tuned hollow wires.
In lower, but still high-ish frequencies, like audio and low R/F, use of many smaller wires (strands) compensates. So, stranded wire has two benefits: greater flexibility and lower AC resistance.
Here's more info:
http://en.wikipedia.org/wiki/Skin_effect