if you're referring to the hose by the oil fill cap, i dont think you'd be able to clog it AND have a still-running motor. Reasoning is that if you can have enough crap and deposits in that 1" thick hose to keep the oil from going back down from the valve covers, imagine what the rest of the engine looks like.
so i'm going to venture the guess that your mechanic is feeding you a line of bullcrap
I learned that whenever a "professional mechanic" tells you something, they usually are exagerating. If any oil passage is blocked, than your motor won't be running for long. But if a passage is only partially blocked, a motor can run on a really low amount of oil. I have learned this from experience
I'd have to go with cam covers leaking. A common problem which you can fix yourself if you have a couple of hours. Get some new gaskets, clean everything up, and put the new ones on without gasket sealant (this is what Toyota recommend, although many people will disagree.) My feeling is if you use sealant, the gaskets do not seat properly. Hand tighten to 13 INCH-POUNDS. Do not over tighten or you will deform the gaskets. You might want some lock washers on the machine screws, or get some small self-locking nuts and bolts.
Clean the spark plug wells out while you do this, and change the plugs so you don't have to take everything off the top again soon.
I say KEEEEECK HIM IN THE BAALLLLSSS!! Business must be slow or your mechanic is a dolt. Tell him to change out the muffler bearings in his car can fix it yourself. NEVER go to a place that lies or is dishonest.