I've read some incorrect statements here...
Yes, you need a dev center account (or other "unlocks"...) to side-load apps. But, there are 2 types of XAP files...
a) XAP built with visual studio... these are unencrypted and can be side-loaded;
b) XAP downloaded from the web store... these are encrypted and need a key from the store to be installed.
The (b) files are the ones you can install putting them on your sd card. But, because they are encrypted and it needs a decryption key to be installed, you need to be online and install them through the store.
And, if the application is not listed in the store anymore, the store will not allow you to install it.
Concluding, if you don't have the unencrypted XAP (which is usually owned by the developer only), there is no way to re-install an application you purchased which has been removed from the store.
And considering you haven't paid for an unknown limited-time license, this is not correct.