People confuse PPI (pixels) and DPI (dots) all the time. Yes, a press might run at a higher DPI than 300, but a 300-400PPI image is generally considered sufficient for even coffee table book-quality printing.
A 300ppi screen that fits 300 pixels into an inch is exactly the same as a 300dpi printer that can fit 300 dots of its laser into an inch of drum.
The difference comes because screens can directly vary the colour of an individual dot. Printers can't -- ink is either present or it is not. The way you get around that is by varying the size of the dot, in a process called halftoning.
Halftone dots are very small, and are arranged in patterns you'll recognise if you look at newsprint photographs close-up. You measure the size of the screen in LPI -- lines per inch, the number of lines of dots (at max size) that can fit in an inch.
Because of the need to vary the size of the dots, on a 300dpi printer you end up with a very coarse line-screen of about 60 LPI. This looks rotten, and so printers go up to resolutions of 1200+dpi. This means you can have a linescreen of around 150lpi, which is good enough for most printing. Each line roughly equates to 2 pixels, and hence a 300ppi image is sufficient for printing, regardless of the resolution of the image or platesetter.
But this doesn't mean there's a difference in ppi or dpi: they're still exactly the same.
* DPI is print resolution, a property of prints and displays
* PPI is image resolution, a property of printed and displayed images
* LPI is halftone minimum printing resolution, a property of printers
PPI is taking a digital image and saying "I want it yay big", LPI is saying "I'll do it by drawing at least this many differently sized dots of entirely different colors", and DPI is going "This is how many dots I'm counting you did it with".
edit: Apparently, some manufacturers of small LED displays like to report DPI as the number of LEDs per inch - that is, 3x the native resolution for images. That's a good example for people like me, who know little about printers.
There's no technical difference, however.
I don't care about the dot density, as long as there are enough of them; I care about the dots/pixel, and deeply about the actual inches. I ran into this problem as a kid, printing some images that had dpi metadata that the printer took literally, but I didn't know how to fix it back then so I ended up with a thumbnail print. Attaching ppi (!) metadata to images is stupid anyway, since the actually relevant information would be the inches (or the dots/inches, for designer decrees).
There is a distinction, and I'm all for precision in language, but it's nothing more than a language distinction for the sake of clarity.
It is not a technical distinction, is my point, and people like Bray aren't wrong to call this a 300dpi display. The worst you can say is they are slightly less precise in their speech than is optimal.
It seems to me that a lot of people do draw a line between pixels and dots, and that a lot of people don't (but usually mean pixels). I don't know if there are proper authorities for this, but I consider the distinction important enough to warrant specific language. My dictionary here says that pixels are onscreen dots - I used to think the same, but now I consider pixels to be the samples in memory. I think you are with the dictionary, since you used the term "physical pixel". My adopted distinction meshes well with my ability to change the resolution of my desktop, measured in pixels, but not the resolution of my display, measured in dots.
I agree that Bray can call it a 300dpi display - I didn't criticize him for it - and I explicitly translate that to a 300ppi natural resolution display. As noted above (according to Wikipedia), some manufacturers are now exploiting this by reporting such displays as 900 dpi, counting the subpixels as dots. Therefore I consider it important to state natural resolution ppi numbers for devices with natural resolutions, such as LCDs, and dpi resolutions for devices that don't have a natural representation of a pixel, such as CRTs. Representation numbers, ppi and dpp, I have yet to see anyone provide (maybe because there are too many resolutions already).
tl;dr: It's confusing people, so make the distinction if you can.
You yourself show the interchangeable nature of dots and pixels when you say you measure the size of your display in dots, even though (assuming it's not CRT), it's very much measured in pixels, regardless of the resolution you've got your desktop set at. (This whole thing came about because of people saying Bray was wrong to measure his screen in dots, after all).
tl;dr: you can insist on a distinction between dpi and ppi, but it doesn't really get you anything, and it definitely doesn't help people understand printing!
So dpi is equivalent to 3ppi for LCD under my definition, and both 1ppi and 3*ppi dpi counts have been sighted in the wild. Using my definition is like using SI mibibytes; when you see dpi you don't know which is being measured, but when you see ppi you can be sure, since ppi is only used by people like me.
As such, I do not consider dots and pixels interchangeable; pixels are what I'm trying to represent, dots are what I'm representing them with. If I'm dealing with a printer, I acknowledge that I'm not going to get neat square pixels no matter how hard I try; instead, I'll end up with round, scattered dots. So I look at the dpi of the printer and the ppi of the ideal representation of my image (in inches), and get something like 6 dots/pixel. I consider this sufficient to render a close approximation to a tiny square, and proceed (actually, I don't usually look at that number, since printer resolution is never a problem for me).
This lets me focus on the one aspect of printing that actually matters to a computer: megapixels. As long as I keep the ppi ratio of my layout high, and trust that the printer has high dpi and proper scaling, I get to ignore stupidities like jpeg dpi metadata. In theory, anyway - occasionally print houses request specific dpi, which can be considered a ppi hint and used to do rescaling with the algorithm I want.
Disclaimer: I've never done any print or layout work.