If it's exactly as described, no; bad idea.
If he actually means a primer doctored with additional oil, well, ok maybe.
Sometimes I double prime: a doctored primer diluted with extra oil and turpentine, then a coat of regular oil primer, then acrylic finish. This can sometimes help paint stick to very dry wood, but the surest treatment is to sand off the weathering, then prime normally. Really deteriorated stuff has to be epoxy-treated or replaced. Sanding can help winnow out the worst spots. Surface treatments are not a cure-all.
Applying finish paint directly over wood that has been treated with pure linseed oil is not a recipe for success, IMO.
Casey

Thanks for the explanation. This was a relatively brief front porch conversation, and he may have left some information out. I've been dabbing paint samples on the walls, which has made me very popular with the trades - LOL!

Hey Gray!

Most Linseeds are VEEeeeeeeeeeeRRRRRYYY slow drying oils.

As Sombreuil gets at...if the wood is sketchy, SAND IT, and remove dust. NOW you've got a sound base that'll hold paint.
Double-priming can help a LOT.

How's the insulation-level and vapor-migration in your house?

Faron

I don't know, Faron. There are plenty of air leaks in the house, but I don't get a sense it's through the walls. It's at the floor and around doors. I saw your other thread on this subject - lots of good info there. Thanks!