It's a case of "empty vessels making the most noise"
Those who make a racket about telling people where they should and shouldn't be, generally have it completely wrong, Like the bus driver who came beeping behind me then trying to force me out of my position (a few yards from a red light) close enough for me to hit the door open button, shouted that I should have pulled over
But no, if there is a cycle lane you are not obliged to use it, though you are free to CHOOSE to use it if you decide it is more convenient to.
In much the same way as a bus driver is not obligated to use a bus lane, it's a "other vehicles KEEP OUT" rather than a "cyclists STAY IN"
You may hear the term "mandatory cycle lane" - again use of this by cyclists is not mandatory, keeping OUT of it by others is what is mandatory
Cycle paths like the one you describe are perfect for parents taking their youngsters to school on their pavement cycles, and not at all suitable for normal riding, so it seems like you have the right idea