Having a read of the California State Athletic Commission rules @Fenster posted I noticed there are some subtle but important differences with the rules of other bodies.
The CSAC rules leave much more room to interpretation about what is 'down' and the counting process generally.

The BBBofC rules, for example, regarding the issue of when the count is beat are quite clear -

3.32.1 In this Regulation 3.32, “down” shall mean one or more of the following:-
(a) when a Boxer falls from the boxing ring beyond the ring apron as a result of a legitimate blow; or
(b) when a Boxer is on one foot or both feet and at the same time any other part of his body is touching the floor of the boxing ring; or
(c) when a Boxer is supported on the ropes of the boxing ring and, in the opinion of the Referee, is unable to defend himself; or
(d) when a Boxer is in the act of rising

and in all of the above cases, a Boxer shall be considered to be down until he has regained his feet within the boxing ring and is in a position and a condition to defend himself.



So when I said earlier that that video actually shows Fury not beating the count, it seems I was applying BBBofC (and others) rules, ie that just being upright by 10 does not mean you beat the count.

If we aren't talking about beating the count, but rather the amount of time taken after the count, the CSAC say "If the boxer who is down arises before the count of ten, the referee shall evaluate his or her ability to continue. If assured that the boxer who has just arisen is fit to continue, the referee shall without loss of time, order both boxers to go on with the contest".

'Without loss of time" there seems ambiguous. But I think most would see the couple of seconds given to assess Fury as being perfectly reasonable.

Either way, I think its a non-issue. It was right that the fight continued.