Let's analyze the options to identify which statement about arteries and veins in humans is NOT correct:

1. Arteries carry blood away from the heart, while veins bring blood towards the heart.
   • This statement is correct. Arteries transport blood away from the heart, while veins return it.
2. Pulmonary arteries always carry oxygenated blood while Pulmonary veins always carry deoxygenated blood.
   • This statement is NOT correct. The pulmonary artery carries deoxygenated blood from the heart to the lungs, and the pulmonary veins carry oxygenated blood back to the heart.
3. Arteries have thicker and more elastic walls compared to veins in general.
   • This statement is correct. Arteries have thicker and more elastic walls because they need to withstand the high pressure of blood flowing from the heart.
4. Arteries do not have valves, but veins do.
   • This statement is correct. Veins have valves to prevent backflow of blood, while arteries do not require them because of their thick muscular layer.

Therefore, the incorrect statement is: "Pulmonary arteries always carry oxygenated blood while pulmonary veins always carry deoxygenated blood." The correct distinction is that pulmonary arteries carry deoxygenated blood, and pulmonary veins carry oxygenated blood, which is the reverse of the systemic circulation.