Yea, you can with the Brick n Mortar sites, but these unregulated online gambling sites are all the same. You just close your eyes and hope for the best.

< So pointing fingers to Freebitco.in would be unfair, because most of them are doing it this way >

The distinction isn't bricks and mortar Vs. on-line it is fiat Vs. Bitcoin.
Bitcoin is very much a libertarian project designed to allow people to make financial transactions without interference from government authorities. Anonymity is very important to service providers.
When I declare my income with the tax authorities or when they do a audit, they want some kind of paper trail and with sites like this, it is not possible. Some of the investment sites I deal with, have "reports" that I use in PDF format for tax purposes.
It should be adequate just to save screenshots. I have investments in other gambling sites and it is my responsibility to collect and save the data there as well.