Agreed, and I think I never said so. We should stick to the terms in place as the topic is kind of complex.
But well, in fact it's quite easy:
Player A has a contract with club A at association A. He needs to be registered for his club at his association to be eligible for matches.
If this player A wants to play for club B at association B - no matter if on loan or permanently - he needs a contract first.
To be eligible for club B he needs to be registered at association B. Therefore club A has to sent an ITC (international transfer certificate) to club B, which will pass on the ITC to association B for registry together with the new contract and the player passport.
On a player passport you can see the list of clubs the player was registered for since being 12 years old
(in order to pay former clubs a training compensation or solidarity contribution before the player is turning 23).
On top of all this you have the FIFA rule: ""A player may only be registered with one club at a time."
How could a player be still registered for club A although he has to be registered for club B to be eligible in a different association? How?
The ITC is giving away the right to be registered at a different association.
Courtois at Chelsea is a well known example.
The Belgian - born 1992 - joined Chelsea in 2011. He joined Atletico Madrid on loan till 2014. After turning 21 he does not count as homegrown.
http://thechels.info/wiki/First_team_squad
Any example of a player on homegrown status after being on overseas loan would be very welcome!
I am not aware of any.
Courtois only signed for Chelsea when he was 19 so wouldn't qualify as homegrown regardless of any loan ( I think )