The only 'speculation' appears to be in just how small a non-zero probability a quantum event can have. If there were actually no lower limit then quantum immortality would (more or less) be implied.

I think the speculation in QI are mainly in the two following hidden assumptions (even if you believe in vanilla MWI) :

• There will always be some nonzero probability event that lets you live on.
• The accumulation of such events will eventually give you an indefinite life span

Both of the above two are speculations and could very well be wrong even if arbitrary low probability branches continue to exist.