Because contrary to what other people likely think, I'd wager Sony is getting their weekly sales information from VgChartz as one of their sources (There is a huge difference between VgChartz reporting sales weekly and Sony knowing what they shipped weekly). This weekly information ensures that production levels are adequate, etc. So it is really in Sony's best interest that VgChartz be accurate.
Sony does use vgchartz data, or at least at one point they have according to the ad for vgchartz pro and as you say it would be in their best interest to give the site enough information so that its data can be as accurate as possible. However, given this places track record of late it seems apparent that their methodology has become outmoded. A margin of error is of course to be expected but the fluctuations in the past months have been severe, to put it midly. Right now it is in vgchartz best interest to update their process or companies like sony may cease using their services in kind, and that is of course a difficult process that will not change overnight. However, vgchartz doesn't look so good right now and it hasn't for a while now.
To expand, I trust sony, as I would nintendo or microsoft, insofar as a broad estimate is concerned. They know how many units they have produced, they know how many they have shipped and they know how many orders that they have received; add on top of that the sales data they have access to from npd, meaa, tsutaya and indeed vgchartz itself among others to help analyze the trends and I believe that information sufficient to extrapolate a rough estimate, given with a significantly larger margin for error. In fact it is in that vein as to why I am inclined to believe them even more. Given the potential margin for error for them to word the statement explicitly that it is over 10 million sold through it would be imprudent of them to say such if the margin of error could even possibly leave the number slightly under that, let alone substantially as the current number vgchartz is quoting would suggest. Now could sony still be incorrect, or worse, dishonest about these number? Of course it is possible, but I feel it is highly unlikely at this juncture..
Now that said, I want to say that the staff having not shut this thread down or heavily moderated its content (at least so far as I have seen, I have not monitored this thread much I admit), and that ioi himself has been open to the criticism, respectful in his replies to the concerns of the community and transparent thus far in his efforts to ameliorate the problem at hand is commendable and I hope it continues.