Web designers aren't photographers. They want to piddle around with editing JPEGs but I doubt they understand what that means. If they insist on JPEG, then give them JPEG. For your situation, it's probably the easiest route, but not the highest quality route. There's nothing wrong with JPEG if you have everything perfect in camera and your post processing is minimal. But for that to happen, you have to know what you're doing at the time of capture. You have to understand and control the fundamentals. You can bend JPEG a little, not a lot. It's a painting that's already dried. What if your white balance is off and the picture has a color cast? Trying to take that out in JPEG degrades the image. What if it's not exposed correctly? Correcting it will introduce noise and fiddling with contrast adds banding. I don't recommend viewing RAW as a fix; it should be used as a platform for greater development potential. But these are real problems that I've seen come into play even with careful JPEG editing on perfect exposures. If you want to shoot RAW, however, you need something to edit it with and you should understand post processing.
If you haven't mastered the fundamentals of photography, RAW is a better bet, but you still have to know how to process it. You probably know the white balance, exposure and sharpening benefits of RAW, but cameras actually aren't capable of producing accurate color in every instance. It may look great, but until you compare it to a color profiled image, you don't know how off it is. If you require the most accurate color, you can do color profiling, which you can't do with JPEG. This instantly sets your color where it should be under the spectrum of light, and colors will look natural. You can export a JPEG to be used on the Web. The other problem with JPEG is it's always finished. If new software comes out that enables you to manipulate RAW in a new way, it won't apply to JPEG. You simply can't go back into JPEG and change the original settings. If you could, it'd be RAW.
If you don't think there's a visible difference between JPEG and RAW out of the camera, you shouldn't be teaching people about this topic. JPEG is a processed file. The camera applies a color space, white balance, contrast curve and sharpening to the file as it's recorded. RAW is an unprocessed file. It has no color space, no sharpening and no contrast curve and thus looks different than JPEG right out of the camera. In fact, RAW usually looks flat compared to a JPEG copy. The changes are applied to the RAW file only upon export. The reason RAW may look the same as you review it on the LCD is because it's a JPEG of the RAW information.
Jay Maisel: "I don't want to look at RAW because RAW looks like s#&!" If you want to argue, argue with Jay.