The second part is also correct, blockchain.info is just a company. If they ever go bancrupt, or just disappear, a lot of people using the blockchain.info wallet will potentially have problems accessing their wallets (unless they made proper backups). But this has no impact on your paper wallet. You could just import your private key into a synced bitcoin core wallet, or into an SPV wallet like electrum, and you can just use your unspent inputs to generate a transaction without ever needing the company blockchain.info

import your private key into a synced bitcoin core wallet or into an SPV wallet like electrum.