I guess his reasoning is:
When you spend your bitcoin, it is essentially you send the bitcoin to coinbase/bitpay, and the sites sell bitcoin.
The more people spending their bitcoin on Tiger Direct or Overstock, the more selling orders are set up.
Pretty much that. Keep in mind though, just because they are using coinbase or bitpay doesn't mean they necessarily have to sell. That is an option in the APIs. Overstock's CEO for example, recently said they won't necessarily be selling all their coins and will be looking at using them to pay employees and suppliers.
Up until now these companies have been selling up front. If that changes and they start holding or building up a supply chain of vendors (and employees) who receive Bitcoin then the whole thing becomes more useful and more people will want it.
One issue (good or bad depending on how you look at it) with the Overstock and Tiger Direct is they get the companies into the headlines but since they don't offer the customer any incentive for using Bitcoin, usage will remain quite low. With credit cards many get points, frequent flier miles, cash rebate, etc. For the customer in these cases using Bitcoin is a loss. These companies need to share some of the payment-processing savings with the customer, not try to keep it all. (A counterexample is Gyft, which gives a 3% rebate for bitcoins -- that is probably too high, but a good deal for buyers.)
It's not like BTC are just sold at the exchange by a shop and price goes down. That would really only apply if somebody took a chunk of their BTC savings (meant as savings indeed) and bought some goods and never bought BTC back to fill up his BTC wallet. Which is the rare case.
You have no way to know how rare that is or isn't. There are certainly people with moderately large to very large holdings from anywhere from six months to five years go who don't need to refill their wallet just because they spend a little. There are also people who need to buy every bitcoin they use. But as I explained earlier this latter group doesn't benefit from paying with BTC at Overstock or Tiger Direct; they are better off using a credit card.