Fluoridated toothpaste is a great additional source of protection for your teeth against decay. It is like having airbags in addition to seat belts in your car.
The mechanism of action of fluoride is through physical contact with your teeth. Fluoride chemically reacts with the enamel and forms a stronger version of enamel, which requires a stronger acid to dissolve.
Ingested fluoride, which would be from drinking tap water, ends up being released in our saliva. The concentration of fluoride in tap water is 0.0001%, so the residual amount that comes with the saliva is very low.
In adult toothpaste, the strength is 1000 times higher than in tap water. The higher availability of fluoride in the toothpaste will have a dramatically stronger effect than the relatively minuscule amount from the saliva. The benefit of using fluoridated toothpaste is much more than fluoridated water.
As a side note, the fluoride treatment that you get from the dentist is 12.5 times stronger than regular toothpaste! Too strong for everyday use. That's why it is only used once or twice a year at the dentist.