Hi Arindam,
Some info on our environment and then I will confirm the scenario:
-Exchange 2016 Hybrid mode. All user mailboxes in cloud.
-We have "Centralized Mailflow" enabled. My understanding now of what this really does, is a process in the tenant look at a message during transport, and if it hasn't come from on prem, it's sent on prem (even user to user - cloud hosted mb to cloud hosted mb)
-Our MX records point to an on premise SMTP relay.
-These relays pass email to our on premise Exchange servers, which then transfer it to the tenant.
Scenario:
-All users are in the same cloud tenant. Boss1 had delegate User1. Boss1 has set up his delegation such that notices are forwarded/copied to the Delegate (user1).
-Boss1 gets a meeting invitation from user2 (a tenant mailbox user) and delegation forwards on to user1. User1 receives it.
-Boss1 gets a meeting invitation from an external sender, and his delegation configuration forwards it to user1. User1 does not receive the message.
-For User1 to get these messages, we had to add an exception to the transport rule of "Is message type 'Calendaring'"