I voted 'no' because it's a trick question. Sharing the road always has to involve give and take and a competent cyclist always chooses the correct lane position (rather than 'any lane position') for a given situation. Sharing is not a thing any road user can do at all times. There are times when every vehicle has to take control of the lane for the very reason that it's safer to do so for everyone involved. If I ride right in a left turn or straight-ahead situation at an intersection, I am not acting safely. In the former instance I am acting illegally, while in the latter instance I may even be needlessly denying vehicles access to a right turn when it would be better for everyone if I took the central or left part of the lane and let cars through on the right.

The question's bias is shown by asking the same question in respect to automobiles: "Should competent automobile drivers drive safely left to share the road with slower traffic?" The question forces people who answer 'yes' to accept a more confining definition of safe and competent driving (presumably laying a trap to allow a straw man argument in response), while the question attempts, by its wording, to make a 'no' answer look selfish.