Nick, it looks like your pic shows transmission wires on top and distribution wires below. Am I right? Alabama Power at times does this along streets in town, running 44KV on top, 7.2KV below. I'm not sure where the defining line between transmission/distribution lies, but we always defined distribution as the lines that distributed the power to homes, therefore the 44KV would be classed as transmission lines, though not near as large as the ones on towers.
*Edit: I see you're calling them primary and secondary distribution. I suppose it's six of one, half-dozen of the other....
I have climbed a few times in situations where I could have stretched out and touched the primary, always in yard situations where we weren't getting our normal 15' clearance. In yards, we were pretty limited to what the customer agreed to. In the case of the hard-headed ones who wouldn't grant much clearance, we assured them that if/when the tree(s) in question ever caused an outage, their power would not be restored until the problem was resolved. It usually worked, but not always.
Alabama Power is usually pretty good about dropping service lines, though they are often running late. I have dropped the service myself on four occasions that I can recall, and have had to put them back up twice. Once, the reconnect was done hot, as I had no way of killing the transformer. With the new radio transmitting meters, self-dropping is a thing of the past, as the computer sees immediately when the meter goes off-line. I looked at a job with Carl the other day where I may have to climb the pole and drop a service wire to a yard light. It'll depend on how accommodating the light company is.