BGP MED Non-Transitive Question

I don't know since I don't know the case they are referring to.

The discussion is over 10 years old so whatever example or case was being discussed seems to be gone.

The key point seems to be "If the NLRI MED was applied on advertisement such as a route-map on a network statement then it will not be advertised as this would be traversing an AS boundary. Policy application is key when working with non-transitive attributes."

Since we can't see the config in question, it is unclear what they mean but I assume they might be using a route-map to qualify a network to get an AS-Path prepend or to apply a MED (metric) that would reliably be used by an eBGP peer (assuming no other interference) or they just mean that they are specifically modifying the advertisement to the peer rather than expecting a received MED value from another iBGP or IGP peer to be preserved and respected by an eBGP peer (for which any transitive or non-transitive will be optional at best).

This example might be more useful:
Or this case study:

The MED survives one AS hop. So if AS1 sends a prefix to AS2 with a MED attached, AS2 sees that MED but removes the MED when it propagates the prefix in question to its neighbor AS3.