So if a team goes 11-0 and dominates all season, and loses to a team that was 7-4 in the FCS playoffs, and for argument sakes, let's say the two teams were in the same conference. Is that producing a "truer national champion"?
In my opinion yes because of what I what I wrote before. Champion and "best team" are not necessarily the same thing and I don't think the point of a championship playoff should be to identify the best team. Sometimes, maybe most times, there is no single "best team." A lot can depend on who teams match up with and how they match up with them. To me a true championship system includes the principle that every team in the realm controls its own destiny. And FCS is very close to that. All but one of the conferences have auto bids so every team in a conference except one controls its own destiny. And if you go 11-0 then lose in the playoffs under circumstances you describe you had a chance to control your own destiny and didn't get it done.
Teams get into the tournament then the last team standing is the champion. And it's a true champion even if it's not the best team.
The new FBS system doesn't approach that. Not only will the majority of teams not control their own destinies, NO team will. Yes, teams in some conferences will have a really good shot. Like the SEC champ is close to a shoe in if they win all their games. But there's no guarantee. It depends on how other teams do and what the selection committee thinks.