You have it the wrong way around. Poorer countries cannot compete with massively subsidized, industrial-scale food production. It’s a known problem that African countries get their markets flooded with cheap European produce, since European farmers are incentivized to produce as much as possible. The surplus is exported.
I actually had a different documentary in mind, but this source is what I have at hand right now. It’s German but the auto-translated English subtitles are accurate.