This is just plain ass wrong. Why would you make a claim like this which you obviously haven't verified in any way?

The shallower your angle is (like on a small cyclocross frame), the more reach will be affected by flipping. The steeper it is (like on a tall road race bike), the less reach will be affected.

But just for sake of numbers, lets do the math for a shallow 71.5 head tube all the way to a steep 73.5 headtube (numbers are for a 120mm 6 degree stem):

shallow:
flipped: 120*cos12.5 = 117.16 not flipped: 120*cos24.5 = 109.20mm (diff is 7.96mm)

steep:
flipped: 120*cos10.5 = 118.00 not flipped: 120*cos22.5 = 110.87mm (diff is 7.13mm)

So you might say for all typical bikes, flipping a 120mm 6 degree stem will give you a 7 to 8 mm reach difference. That's pretty damn significant.