This is completely false. No browser that I know of does any such thing, nor would it make any sense to do so (nor would it achieve the goal you specify to any meaningful extent).
The closest thing that does happen is that browsers use integer fractions of pixels as their basic layout unit: Firefox and its kin sixtieths, Chrome and its kin sixty-fourths.
But the rest of your answer is correct; and to add a proper citation: “the reference pixel is the visual angle of one pixel on a device with a device pixel density of 96dpi and a distance from the reader of an arm’s length” <https://drafts.csswg.org/css-values-4/#reference-pixel>.