As mentioned before by others, I believe it originated because the British O Gauge is 1:43.5. Still doesn't explain the precise 1:87.1 that HO is, but the 0.1 is always rounded down to 0 to be 1:87, or that the British HO is 1:76. But then, to use another example, N Scale in the US is 1:160; 1:150 in Japan, and 1:148 in the UK. The wonderful world of model railroading!!!
That's because HO scale is exactly 3.5 mm to 1 foot. Do the math with a scientific calculator, and even 1/87.1 is a rounded off figure.
Matter of fact, British O-scale is exactly 7.0 mm to the foot. And likewise, 1/43.5 is also a rounded off figure, even it is not exact.
But to heck with the math, we're just splitting hairs at this stage. My advice is to go run our 3-rail, 1/48 scale (sorta' kinda', more or less) O-gauge trains and let the HO and N-scale guys squabble over exact dimensions with their micrometers and their rivet counting.