it's not hair splitting, but correct.
LR is actually designed for photographers as a workflow and processing application, and PS is designed for graphic artists for myriad of different applications.
You need Adobe Camera RAW to processing raw files in any sort of easy manner within PS--which is pretty much a LR plugin for PS.
I strongly suggest using LR for processing photos. Beyond just being able to quickly adjust the image, you can organize, categorize, metatag, batch process, reject, flag, rate, before really even touching a single image. It's a great tool for photographers that don't need to manipluate pixels. And if you need to bring things into PS, you can export directly to PS, alter the image, but keep the file within the LR workflow so the changes are reflected back in your LR gallery.
Like I said, I've been using PS since PS2 or PS3, roughly 1995. As far as my photography is concerned I use pure LR about 95% of time. At work, doing UI/Graphic design I'm in PS/Ill about 95% of the time.