In looking for an 'authoritative' answer, I found....
http://www.treasury.gov/resource-center/faqs/currency/pages/legal-tender.aspx
While it is not a direct answer, it is interesting.
Other resources are certainly as vague on the subject
http://en.wikipedia.org/wiki/Legal_tender
as well they should be, since "legal" can vary from state to state, and "tender" is also a topic unto itself.
More directly to the point, it seems (in your 'underlying question') you are looking for a way around 'the system'. You, of course, are not the first one with such an idea, and the hundreds of thousands that came before with such a 'scheme' have already been viewed and analyzed by 'big brother' - or, they have found other methods, once they reformed the question.
What you are asking to do is be "paid" in gold (by your use of the word 'payment') - which is not a legal tender in the US (though is now legal in some states - which are separate from the federal law [if you do not understand this, you should do some research....]).
While you perhaps could 'exchange' the silver for gold (as you are asking for a similar value amount, with no profit or loss), it would be considered a BARTER transaction, which is governed by different laws (much like if you had asked the question "Can I be paid 12 chickens for my 1 horse?" or something.....). Again, research barter laws in your state, as well as federal laws. One of my relatives does an extensive barter business - I've seen "cash" transactions from them on very few occasions over the last 25+ years, so it is certainly possible.
Note that such a transaction (i.e., barter) would also have to be standard policy for the other person/business, which also must keep track of such barter transactions. Most large businesses in the US (i.e., the 'refinery' you asked about) do not make such transactions (primarily, from what I have seen, it is because the 'bean counters' don't know how to handle them), however, they would make two transactions for you (converting everything to legal tender in between). There was a 'Pawn Stars' episode where a man wanted to sell his car for gold (couldn't find the video online, but a search for "pawn stars man sells car for gold video" brought many links....) - they bought the car for cash, made the man touch the cash (transaction complete), then sold him gold for the value. The nice part about buying gold in Nevada is that if you buy bullion, there is (currently) no tax, so you do get a lot more gold for the cash.
Smack also gave you a good, 'creative' answer, though, in this instance, the transaction would be treated as securities, which are legal tender, treated under another set of laws, and could potentially create a taxable event (this is a term you should understand as well) - ask your accountant about "taxable events".
What I believe you are looking for is a way to eliminate and/or avoid these - lots of creative ways, but you have to be careful, understand the laws and rules and also (and very importantly) "live the life" when you choose to go that route (this goes into great depth, even so far as to how you word your statements/questions ==> when you use "payment" and "bullion" in the same sentence, that's a red flag for any auditor!).
So, like most of the theoretical questions on this forum, there is no direct answer to your question. However, there are ways to create what you are looking for (from what I believe to be your 'underlying question'), you just need to be more direct in what you are asking.
Most likely, once you have 20K in silver you are looking to sell, you will have studied such options more thoroughly and will have a decent understanding of the ways, laws and methods and be ready to discuss these options more directly.