A third party doing the stats would be fine, providing they have enough resources.
The Advertiser stats are not up to scratch because they only have two people doing it (one for each team) and they do it the old-fashioned way with pen and paper. The quality of the clubs statistics are much better because they

use laptops with specialised software to record the stats (most if not all clubs do this now)

they have more people involved - specialised callers who get to know the players very well, and specialised keyboard enterers
I don't believe that clubs fudging stats on purpose would be an issue. As May-Z said we take the accuracy of our stats
very seriously, and from what I have heard/seen most of the other clubs do as well.