This is true. The timing/necessity of the oath to assume presidential powers has been a subject of debate for centuries.... for example, if LBJ had needed to make a crucial decision after JFK's moment of death but before they found someone to administer the oath to him would he have been able to, etc.

While there was nothing wrong with Biden taking the oath ten minutes early, it was yet another odd thing about a day filled with very odd things. Not illegal or improper, but it could be significant.