What you read wasn't necessarily correct.

A good hybrid with appropriate tyres can be very fast indeed. If you have a yucky hybrid, replacing it with a good one is probably a more reasonable thing to do than buying a real racing bike, which will be more delicate and less comfortable... and road bikes that aren't real racers are, generally, these days known as hybrids. It's a marketing thing.

Main things -

- Put proper high pressure slick tyres on your bike and keep them pumped up. About 1.5 inches width is right, but you could opt for 1.25s if you want to be a real speed demon.

- Keep the chain clean and derailer adjusted.

- Put clips or Power Grips on the pedals.

- *Maybe* adjust your handle bars so that you're less upright and more streamlined. Make sure you can still see and steer comfortably!

(The above is pretty much a typical courier bike set-up.)

If the hybrid is a good one and you still want to go faster after that, consider changing one of your gear rings if you're spinning out while pedaling, and *maybe* fitting Midge bars (mtb drops) for a slight aerodynamic advantage. These things are much cheaper than buying a good new bike, even secondhand, and a poor "road" bike will be slower, less comfortable, and not as safe.