Not some home brew theory. And it is very convoluted, but it's bascially more "one China" policy word games.
The Taiwanese president unofficially stated in 1991 they do not claim mainland China, but this was never affirmed by courts and there's no force of law behind it. They cannot officially do this currently without greatly antagonizing China. China's view is that Taiwan limiting its borders to include only Taiwan and not all of China, would signal the end of the "one China" policy and be a precursor to Taiwanese independence. If Tawain were to declare different national borders that include only the island itself, then China would view it as a violation of their anti secession law passed in 2005, which threatens military force in retaliation. In China's view, they are another government still within China and still in civil war, without the authority to re-define national borders.
https://en.m.wikipedia.org/wiki/Anti-Secession_Law
Continuing to claim mainland China as part of the same country is continuing the current status quo, any deviations from that would be viewed as an attempted separation of "indivisable" China. So the claim to the mainland at this point in history is primarily to not antagonize China and continue the status quo situation.
