Linking Sharekhan and Zerodha Trading account with same CDSL Demat account

#1
Dear All,
My Current broker is Sharekhan and i have a CDSL Demat account, Opened and operated by Sharekhan. I recently opened an account with Zerodha as it turned out to be cheaper and got my Demat account linked with Zerodha as well. Now, that the account is linked, i cannot see holdings in my Demat account which i bought through Sharekhan in the online software of Zerodha, Zerodha trader. When i called up Zerodha regarding same, they said, since you have linked Demat account operated by sharekhan, in case of delivery, u can only buy through Zerodha and Selling has to be done through Sharekhan only paying Sharekhan's brokerage. Please confirm if this is a valid point made by Zerodha since as far as i know we can link any number of trading account to same Demat account and buy and sell from either of them.