Your understanding is close, they sourced bacteria from puddles that had glyphosate resistant bacteria, then they modify agrobacterium that are specific to whatever crop they are trying to modify. Every cell in a plant has to be able to fend off disease because there is no central immune system. So agrobacterium inject their DNA into plant DNA so the cells think they are not a threat. So, if you have an altered agrobacterium, then those altered genes are passed on as well. BUT, to grow a whole new plant, you have to cut the infected cells out, grow a callus, then grow an actual plant from the callus before it can even produce seeds. Very few plants can grow from clones like that in the wild AND you need to have enough cells that have the same modification for any significant chance of growing a modified plant. So the odds of a single aphid injecting agrobacterium in a cell, then that cell somehow falling off, growing in a medium that can support callus development, then also somehow developing roots in an auxin rich environment, all before the seasons kill it off so it can spread seeds are very slim indeed.

Being that all of the techniques used in the industry are based off of nature anyways, if it is plausible for GMOs to do it, then normal plants have been doing it before GMOs even existed.