Coincover will never pass your information to a third-party unless it has a legal obligation to do so. For example, law enforcement agencies often have extensive criminal investigation powers including the ability to obtain production orders requiring information to be produced. It may result in a criminal offense for any entity supporting Ledger Recover to fail to comply with a production order, but Coincover would always take all reasonable steps to verify a production order before complying with it.
You should also note that the Recovery Seed Phrase (RSP) is encrypted and split into three fragments – all of which are held by independent companies established in separate legal systems. Since a minimum of two of three fragments would be required to gain access to your wallet, it is likely that an order would need to be obtained in at least two jurisdictions. These individual fragments are not exploitable on their own. Two of them would need to be recombined and decrypted, with separate keys. Any order of this nature would realistically only ever be obtained in the most serious cases of criminality (such as where terrorist financing is suspected).
Coincover will never be able to access your seed phrase. Coincover or the other backup providers will only ever manage one encrypted shard. We do not hold nor have access to the other shards that make a complete seed phrase.