If you expected the probability distribution function for the falling to be a poisson distribution with respect to time, it would matter. There may be a time element (from fatigue for instance) but more logically it will correlate with the number of feet of sidewalk or road that the pedestrian has travelled. It's not the same thing, because walking paces vary significantly. I would expect a Poisson distribution with respect to space, not time.

I submit also that causes of bicycle falls are enough different from pedestrian slip and falls, that the same probability functions cannot apply to both.

The upshot is that pedestrian slip and falls, resulting in TBI, have a more similar risk to cycling than you may be estimating. I think that it's better to look at data than to speculate about probabilites.

From FARS data, with respect to fatalities (since fatality data is the most accurate), trips while walking are not significantly safer than trips by bike. Motor Vehicle Crash Injury Rates by Mode of Travel, United States: Using Exposure-Based Methods to Quantify Differences
The chart shows that cycling has about 50% more fatalities per person-trip than does walking, and only about double that of trips in passenger cars. This is from Motor Vehicle Crash Injury Rates by Mode of Travel, United States: Using Exposure-Based Methods to Quantify Differences

So his question remains a good one.