If you read
Sword Coast Adventurer's Guide and You! it makes explicit exceptions for DMG races. Kalani's right, it's just that her rationale was wrong.
The following quote (from the above article) sums up exactly what I was trying to articulate (but apparently failing to)
Races or other options that are mentioned but whose rules are found in another source (i.e. aasimar or genasi) do not become legal without other campaign documentation unless that source is also legal for your character’s story origin.
As I kept saying - aasimar and/or the DMG need to be listed for your story origin, or you need a special certificate (the aforementioned "campaign documentation" mentioned above) in order to use it.
The specific exception mentioned above is not actually a specific exception. It is a restating of a general rule for Story Origins and clarifying that despite the fact SCAG mentions aasimar and genasi, it doesn't add those races to your "Allowed Rules" (primarily due to the fact that the SCAG itself does not contain the rules for such races, and instead refers you to the other rules source - DMG or EEPC in this case).
Put simply - unless one of the following is true - you cannot use a race/class/background/creature/etc with your character:
1) The rules for that class/race/etc are listed in an "Allowed Rules" source for your Story Origin (eg. the EEPC is specifically listed for the Elemental Evil origin).
2) The rules for that option are listed in an article with the "AL Legal" logo (such as the Mulmaster/Hillsfar Backgrounds, or the Brotherhood of Cloaks rules).
3) You have a certificate specifically adding that option (such as the
cleric of kelemvor, aasimar or
steeder mount certs).
4) The rules option was made available in an official adventure (such as the
maze engine effects or the various companion creatures found in
Out of the Abyss).
5) The rules option is specifically mentioned in an official FAQ as being available.