Actually not true. Most VU meters use RMS to display.
RMS also represents much closer "appearent" loudness. Normalizing deals with "Peak" loudness. Two very different things altogether.
Normalizing tracks WILL NOT make them sound the same volume. All's normalizing does is raise the overall track volume up so that the loudest "Peak" volume is 0dBu on a digital Peak meter. You can have peaks that are many decibels higher than the Average, or RMS level of the song. So, normalizing may not bring up the volume of a mix that has very wide Peak to Average levels. In fact, Normalizing MAY not raise the level of a track at all because the track could very have peaks that are too close to 0dBu for you to hear the difference a few tenth of a dB boost would give as a result of Normalizing.
Normalizing is an unneccesary step in the "mastering" process of compiling songs together that will be on the same disk. If you are "mastering" effectively, you will use POSSIBLY Eq, Compresssion, and Limiting to achieve higher average levels and after all that, you will STILL probably have to adjust the overall volume of a song or two from the rest to make them all have the same "appearent" volume.
Ed