In my experience, the emailed statements are usually 7-14 days behind "actual" activity and are essentially useless.
On top of that, while stay/credit card activity (usually) posts in a timely fashion, the overall points grand total update lags by 3-5 business days. As an example, I recently completed my 60th night of the year which earns a 40k point Milestone bonus. The stay/spend activity have posted, I received the congratulatory email, and the HHonors app displayed a "congrats, you've earned 40k bonus points!" notification. My points grand total still hasn't updated. HHonors Customer Care boilerplate response is "please allow 6-8 weeks for this bonus to post."
I keep a spreadsheet of all of my Hilton activity. It's unfortunate that I have to do this, but it's necessary. My grand total hasn't been correct for 6 months. Hilton has been "investigating" for 5 of those months. They've thrown some "service recovery" points my way to make up a portion of the difference, but the total is still off. At this point, I don't care. It is what it is.
If you're 100% sure of a discrepancy, I've found that the Twitter team is the most responsive.