So is this 'fact' true then?
Partly. Well it really depends what source you look at. There are several notable Geological companies/organisations around the world that specialise in analysing minerals and the Earth etc and all the results vary. In fact, if you look at the most recent USGS report from 2011, it now states that there's around 17 billion ounces of Silver left in the crust. So with the world consuming roughly 1 billion ounces per year, that indicates another 17 years before Silver becomes 'extinct'. As I said, different reports issue different figures and after hours of Googling (I made it to page 24) the general consensus does indicate that we have anywhere between 8-17 years left of Silver reserves in the Earth's crust. HOWEVER, we can't just stop there. There's a lot more to this scenario to appreciate.
The USGS wasn't incorrect in stating this, they just lacked a bit of detail to their fact. Either that, or people in general have ignored the finer details. There's a big difference between Silver becoming extinct and Silver becoming economically unfeasible to extract. Despite it's increasing rarity due to huge global consumption, Silver will never become 'extinct'. It will always remain in existence in the form of posh cutlery, ornaments, antiques, electronics, clothing and medicine etc. But there will come a time whereby it's economically unfeasible to extract more Silver from the ground. At this point, to all intents and purposes, (especially for investing) it will have the same effect as becoming extinct. It's at this point where I wouldn't be surprised to see crazy Silver prices like $10 000 an ounce and upwards. Rhodium entered a similar situation between 2004-2008. There was a global deficit in supplies and so it went from $500 an ounce all the way up to $10 000. And Rhodium isn't even half as in demand as Silver.
So how long do we have then?
This is where the USGS is partly correct. There may be around 15 years left of Silver in the crust, but we only have about 7-8 years left of economically feasible Silver to extract (at these current prices). You see there's a common misconception in the rare earth mineral world between rarity and scarcity. Silver is very rare in the periodic table, but it's also extremely scarce. This means that the Silver deposits in the Earth's crust are of small volume and are scattered all over the place. As a result of this 'peppered' location of deposits, it's just a waste of time/effort and money to set up a drilling operation for such a small return. So normally they don't bother. It's like being in a football stadium with loads of 1p coins scattered around it and there's a few stacks of £20 notes dotted around. If you only had an hour to collect as much cash as possible, you'd just go straight to the big deposits of money and would ignore the 1p coins.
Also due to Silver being extremely undervalued and under-priced at the moment, Silver is simply a byproduct of base metal mining operations like copper and zinc mines. These companies just get small amounts of Silver and sell it on for minimal profits. Also a lot of people are unaware of how time and money consuming mining is. From the moment a feasible deposit is found, it normally takes 7+ years to set up a producing mine! So we do effectively have 7-8 years left of Silver available.
BUT...

CONCLUSION
In a nutshell, the USGS were partly correct. We currently have about 15 years left of Silver in the planet, but we only have about 7-8 years left of economically feasible Silver available for extraction. So combined with Silver being far rarer than Gold in investment form, prices need to increase 1000% before dedicated Silver mining operations start and the world is now buying 3 times more Silver than Gold, the next 1-5 years are going to be extremely interesting...
In the meantime, I'll continue building my financial Ark of Silver and Gold in preparation for this economic Perfect Storm brewing in the horizon...