That's actually a bit backwards. A 3-knob with a '62 neck and '63 pots wouldn't have left the factory until '63 - so it's a '63. That's why original solder joints are important... to know that no one replaced the pots at another point in time. The year of the bass is always considered to be the year that it most likely left the factory, according to the last original date you can find on it.
And likewise, based on the info you gave us, you can call your own bass a '61 "because of three ['61] pots"... because you also have a '61 neck date... and a ser # that is still in the '61 range (if that is in fact the case). To get even more definitive, pull the pickups out... my guess is (based on the neck date and those early '61 pots), you'll probably find a '61 body date too!
The concensus is really that 3-knobs are actually a late '61 feature, with some stack knob overlap into '62, while most '62s were 3-knob. I suspect any misinfo going around about 3-knobs being a '63 feature were a resuklt of Fender reissuing the "62 Jazz" with stack knobs - it made most people assume all '62s have stack knobs.