I’ve been a diamond dealer for over 30 years. In that time I have bought countless diamonds from all over the world, but I’ve never yet bought a diamond site unseen (except engagement rings by Tiffany & Co., but that's a different article). There are many important nuances not measured by a GIA diamond grading report and not visible on a video, that will affect the diamond's brilliance and value in real life
Here are some examples:
Tint: Diamonds come in all the colors of the rainbow. The most common by far is yellow. In fact the diamond color grading scale is based on the lack of primarily yellow. Next most common is Brown. A diamond certificate however will not discern between a slight brown or yellowish tinge, For example a Diamond can be graded as an I Color, with a slight yellowish, or a slight brownish tinge. Both will be graded 'I', but the brownish one will face slightly duller and darker, and worth significantly less. To the industry's credit, in the past ten years or so, it's become common for diamond dealers to note this difference, however certificates do not. The only way to know whether the diamond is slightly brownish is for you or someone you trust to see it. Personally, I trust my eyes the most.
Haze: Not all diamonds are made of the same quality material. Some diamonds, all else being equal, will scintillate and sparkle more or less than others for any number of reasons. Grading reports do not grade this slight haziness or cloudiness in a diamond. This is another reason you to see the diamond. In fact, even a trained diamond dealer might not be 100% sure a diamond is a bit hazy until comparing it to a non-hazy diamond. If there is no side by side comparison, it is extremely hard to differentiate and pick out the best and brightest stone.
Inconsistent shapes and facet arrangements: This one applies almost exclusively to fancy shapes. As of yet, GIA, the industry leader and gold standard, does not have a cut grade for fancy shapes (any diamond that is not round is considered a fancy shape). The reason being, they have not yet come up with an algorithm that reliably predicts the beauty of a fancy shape based on its proportions and measurements. AGS labs does have a Princess Cut rating, which I’ve found to be mostly accurate, but all other shapes have no rating for cut grade. There are just too many variables within a fancy shape to take into account at this point. So Fancy shapes definitely need to be seen in person.
SO… bottom line, diamonds on the internet are not rip offs, and it is possible to find a good deal and a good stone, but you need to know what you are doing. Know that you get what you pay for. If you see 100 one carat diamonds listed online and all are "ideal cut", don't buy the cheapest one ... and probably not the most expensive one either. And If you have access to a good local jeweler who you could trust, it’s a great option, even if you end up spending a little bit more, at least you know the stone you're placing on her finger, for the rest of her life, was not a compromise, and is the best and brightest. In 10 years from now you'll be very happy you did.