Absolutely agree - there isn't any justification behind this number.
I'm wary of using the formulas in the machinery's handbook too but don't have any other references to go on for the design of splines. Could you recommend any?
I've just been working through the equation for the compressive stress on crowned spline teeth on p. 2174 of the Machinery's Handbook (29th Edition).
When you put the units in, the results come back as SQRT(psi).
Can this output be directly compared to the stress allowables in Table 11 on page...