Ah yes, selective breeding... also known as the original method for creating GMOs. Nowadays we can just do things a bit faster without all of the waiting required for multiple generations of crops. But that doesn't mean that we haven't been practicing artificial genetic selection for millennia.
Ah yes, validating all GMOs just because we've been breeding cultivars for thousands of years.
Safety not gauranteed:
The solanine heavy Lenape Potato, sure solanine is in all potatoes, but when did a non-green one make you sick?
The "killer zucchini" from New Zealand with dangerous amounts of curcubitan caused by a aphid outbreak in the organic fields.
Mono-cultures can happen:
The Irish potato famine could have been reduced in severity if there were more variety among Ireland's food crops or their potato cultivars in 1845.
While nowhere near as devasting to humanity, the destruction of the Gros Michel banana cultivar and the impending threat of the newest banana-phage on the current Cavendish cultivar aren't exactly a good faith offering on future mono-cultures, GMO or not, being avoided.
You seem to be making two contradicting points here.
On one end, you talk about food safety, and how altering the DNA of a plant means it might not be safe anymore. But in that case, the best thing we could do is to make sure we are always making plants with the exact same genetics: All clones. That's the only way you can tell what you are eating. There are more genetic changes in a naturally bred, not inbred crop than there are in a GMO event vs the untraited plant.
Then you seem to dislike monocultures: If you want the plants to be safe from some phage, nothing better than high genetic diversity in plants, which leads to us really having no idea of how safe what we are eating is.
We either want to treat them as drugs, and make monocultures the way of the world, or we look for genetic diversity, in which case having some BT toxins embedded in your corn plant won't be that bad. Just ask agribusiness to make sure there's at least 8 different germplasms per bag or something like that.
It is interesting that we can accidentally select for poisonous compounds. It turns out that plants can make themselves resistant to many pests; by filling themselves full of poison. These kind of issues are well known. See Conjuring An Evolution To Serve Youhttp://lesswrong.com/lw/l8/conjuring_an_evolution_to_serve_y...
It can happen by chance or convergent evolution. Mutation rates are sometimes artificially raised to increase the probability of it happening. https://en.wikipedia.org/wiki/Mutation_breeding
It's extremely hard to selectively breed fish DNA into a plant. Convergent evolution doesn't end up with the same DNA sequence. My favorite example is the protease catalytic triad, where 20 or so different evolutionary routes have converged to the same chemical function, even though the DNA for those different superfamilies are different.
The odds of mutation breeding producing a new gene (or more likely, changing an existing related gene to correct form) is incredibly small, and the result would be very expensive. Each generation would need to be sequenced, and the ones whose DNA is closer to the target re-bred. You want the mutation rates to be low enough that the rest of the plant isn't killed, so that's what, a mutation somewhere in the target gene every 1,000 generations? Assuming a short sequence of 100 base pairs, and perfect mutation gives 100,000 generations. Assuming a life cycle of 10 days means this will take over 2,500 years.
I deliberately low-balled these numbers.
So yes, "by chance" it's possible, in about the same way that a universe of monkeys could type out Hamlet.
How do these observations lead to a breeding technique where a plant ends up with fish DNA?
You'll notice the the events listed are either in related species, or from ecologically very tightly coupled species (eg, host and gut bacteria), and seem to imply time scales and population counts which are much higher than would be economically feasible for breeding.
Because there's no such thing as 'fish DNA'. There's just DNA. Its a code, and code doesn't 'belong' to any organism or know where its at. So transfer of DNA from one organism to another, like monkeys typing, increases the rate of change in species well above that of mutation alone.