For one thing, I said in the OP that it was our fault the dog got into the trap, not the trapper's, so Thanks Captain Obvious awards to the last few posters. The dogs being loose was a sore spot between me and the wife, in fact. She believed, for whatever reason, they would stay on our acreage, and a friendly neighbor's adjoining land. I think she accepts my argument, now. I plan to install invisible fence when I get home, to prevent future repeats.
That does not relieve the trapper of the moral obligation to check live traps much more frequently. In some states, that obligation is legal as well as moral - I am not sure about Missouri, because I don't trap. Friends from other states do, and have apprised me of some of their regs as an FYI.
For another thing, the dogs are collared, tagged, and microchipped.
Last, grubbylabs, he didn't have to risk getting bit - he could have just called Animal Control. Shooting a trapped dog would have been unnecessary and, as noted, the traps were on public land, not the trapper's property.