How is the statement wrong if LTC does exactly what BTC does and stores start accepting it?
Because LTC doesn't do "exactly" what BTC does. Does every store, exchange, merchant, and user which has, uses, or accepts BTC also have, use, or accept LTC? Does LTC has the same security against a 51% attack (exactly the same security)?
If not then LTC utility is not the same as BTC. It may have utility but it isn't an identical replacement. The concept is called fungibility. Gold for example is a good commodity money and diamonds are not because all pure gold is identical however diamonds (or other precious stones) vary in value significantly based on size, shape, color, etc. All Bitcoins are identical. There aren't good Bitcoins or bad Bitcoins. There are Bitcoins which are slow to confirm and Bitcoins that are fast to confirm. All Bitcoins are equally vulnerable to unconfirmed double spend or 51% attack.
While BTC & LTC may have similar properties they aren't fungible. The value of LTC money supply may indirectly affect BTC exchange rate but BTC will retain its own valuation much like Silver and Gold retain unique valuations. Gold and Silver are both precious metals, have similar properties and have similar uses. Gold however is valued about 50x as high. Under your logic this shouldn't have happened. The price of gold should fall and silver should rise to reach an equilibrium with silver at say $300 per ounce for all precious metals (Gold, Silver, Platinum, or Paladium your choice).
