Jewelry and silverware is generally sold at 100% markup over the raw material. You may be able to find junk silver here and there but there is also a lot of fakes and scams. No company is going to sell you silver at spot. So you could meet random people off craigs list, bring large amounts of cash, and buy their junk silver. Could you determine the purity of silverware? Could you catch fakes? Could you ensure you don't get robbed?
No dealer is going to stay in business selling anything (computers, cars, silver) at material cost. Can you think of any product in the world which is sold at material cost?
So yes if IF you wanted to start a business buying junk silver, grading it, melting it down into bars then you could probably acquire some silver at spot (and get scammed some % of the time also). Of course you need to factor in your time/risk/equipment/capital costs. However no business is going to do all the work (and take all the risk) for you and then give it to you below their cost (material cost + time/labor/equipment/capital costs). Right?
Would that sort of stuff sell at spot value on the second-hand market, potentially?
Probably not. The same issues that applied to you above would also apply the buyer. How does he know it is authentic, how does he determine how much silver content it contains, etc. Why would he want to take that risk.
Even if you sold all your junk silver to an assayer or refiner they are going to deduct something from spot for their time/labor/risk/equipment/capital.