Hello,
Your understanding is not entirely wrong. In simple words:-
* Recipient must maintain the certificate chain if it needs to secure authenticate peer when their Sub-CAs are different.
* Sender can send certificate chain (e.g. Local Cert + Sub Cert + Root Cert) but sender's chain will not be used generally to
authenticate Sender unless receiver has trust relations with Sub Cert + Root Cert. This chain may be used to gather
information like CRL but not authenticating sender.
So just because sender is sending Sub CA + Root CA, I (receiver) will not use those certificates for validating sender unless receiver also trusts Sub CA + Root CA (It has a chain).
Regards,
Rushi