Buzzing pole piece on E string of my P

[pjmuck]

I recently brought my '73 P to my repairman for an overhaul, replacing the pots, input jack, and I also had the original PUP sent out to Lindy Fralin for a rewinding. I picked up the bass yesterday and noticed a buzzing sound coming from the exposed pole piece of the E string's pickup. I normally pluck over the pickup, and noticed that it only happens when my fingers come in contact with the pole piece if I touch it. I called my repairman and he said that Fralin may have only rewound one coil, but that I could also coat the pole with nail polish if I wanted. He wasn't sure if Fralin would redo it without charging again, but he was willing to make the argument that I did send it out for a proper rewind and perhaps they should have checked the condition of the entire PUP and not just half the coils. He did recommend I coat the poles with nail polish. I put a piece of Scotch tape over it just to see what the result would be, and it does cut out the buzz considerably, though I wouldn't say completely.

Should I return the bass to my repairman and have Fralin redo the rewinding, or is this a common issue with a 37 year old PUP and the best I can achieve? It does sound great otherwise, and I could probably live with the result using nail polish, but I can't help thinking that I should have gotten a problem-free PUP back considering I paid for it.