No. Your thinking INCHES. Inches don't exist on a monitor, only pixels. So as you've already stated, in Xara, as you decrease the dpi the pixel dimension reduce. Vice versa if you increase them. Browsers just see the physical dimensions as x pixels wide & y pixels high, and display them as such on screen. So when you reduce the dpi in xara to 72 it decreases the pixel dimensions, thus you have a smaller image, not the same size image with less dots.
Answer me this though - how can a 72dpi image be physically smaller than a 96dpi image? The number is supposed to equate to the number of dots per inch, so the image should be the same size, just have less dots in it.
Try it yourself, create 2 images the same in Xara. Export first at 96 dpi then again at 72 dpi. Now import them into your web editor. They will be different sizes.
The dpi only matters for printing.
HP xw9400 W/S / 2 x Dual Core AMD / RAM 16 GB / 240 GB Kingston SSD / 120 GB Kingston SSD / 500 GB HDD / ATI Radeon HD 5450 / Windows 10 / 64 Bit /
Xara Designer Pro X (12 or 365)