The difference is that a tribute band does not have official members of a band. Schmit and Walsh ARE official members of the Eagles. They're not fans or touring musicians. They're full fledged Eagles, per the band, their management and the contracts. If Don Henley sees them as members of the band, then so do I.
Well first of all, that's a hypothetical that probably would never happen. The Eagles without Frey only happened because Henley is still around. Without any original members, it doesn't typically make sense to tour as that band. And I do understand that there is something to be said for "founding members" whatever that means. But I also think it's dismissive and disrespectful of someone as amazing as Joe Walsh to act like he's some faux Eagle or something. If someone told me Matt Cameron was not really a real member of Pearl Jam cuz he's ONLY been around for 26 of their 32 years, I would have some pretty harsh curse-filled things to say in response. "Well, Mike Inez isn't REALLY a member of AIC cuz he's only been around since 1994, not 1989."
Especially when the Eagles have had additions, comings and goings almost the entire span of their career. Is Don Felder also an Eaglet or whatever someone said? He's not a founding member.