The link you attached lists a few different lead-free solder alloys with the lowest melting at 412F(211C) well above 340F(171C). Eutectic tin/lead solder has a melting point of 361F(183C), also above 340F.

I'm not sure whether or not cracks can heal at temperatures below the melting point, but I would be surprised if that were possible.

So it turns out that home oven manufacturers don't care too much about precision when it comes to oven temperature (and it doesn't matter usually).

A high end home oven will easily swing between +- 25 degrees of the temperature that you have dialed in, and that's if it's well calibrated.

If he didn't dial in "340" quite right, and his oven was average, I can easily see it hitting temperatures of 412+, and that could also account for his varied results.

Not to mention we don't need the solder to completely melt, only soften (depending how badly cracked the joint(s) were).

If this were Mythbusters, we'd call it "Plausible".