There have been two different selection processes, that which concerns the bike planning process, in which certain roads are chosen for bikeways, and the selection process by which Moritz's subjects selected their routes of travel. Beyond these two different selection processes there is the process of installing bike lanes.

I don't know how familiar you are with the bike planning process. Bike lanes start by being installed in those locations where installation is easiest and where the road is already considered safer. Bike routes are even more signed only in those locations that are considered to be safer than others. That's all typical, and must be considered in determining whether the bike lane or bike route sign actually reduced the car-bike collision rate.

You assert that Moritz's subject selected their routes according to their evaluation of the safety of those routes. Their evaluation is quite likely not in agreement with the bike planners; active cyclists differ with bike planners. Even if this selection process occurred in a reasonable way (whatever you may consider reasonable), you argue that this selection would indicate that, for any comparable selection of roads, the bike route signs had reduced the previous car-bike collision rate; and the same for bike lanes. The selection of particular routes by cyclists provides no evidence at all of such an effect.

You argue that widening a road to install a bike lane (which sometimes occurs) has an effect different from that between the narrow road and the wider road, when it is commonly considered that the wider road is safer than the narrow road. That the other changes in the road made as part of some process that includes a new bike lane may be more significant than the bike-lane stripe itself is widely recognized. Hamilton appears to be rather alone in his argument.