Are there engineering solutions in the near future that will allow us to have PHEVs that can be charged either by plugging in or by the petrol/diesel motor?
The future is now. :-) This functionality exists in the Toyota Prius Plug-in (at least in the 2019 model that I drive); so the claim in the article is just false.
In the Prius plug-in there's a "Charge Mode" button, which will charge the battery up to full capacity from the petrol motor while driving (but it runs more sluggishly, and uses more fuel, while doing so than the usual petrol-powered driving mode). It's not clear why you would want to do this, but the option is there.
Even if you don't use this "Charge Mode", if you drive a PHEV without plugging it in, it will still use the battery to "smooth out" the load on the engine – putting charge into it when demand is low, and taking it out again when demand is high. (It just won't charge it up all the way to the maximum.) In other words, it drives like a "normal", non-plug-in hybrid. But because the battery is much larger than a normal hybrid, you get an additional efficiency gain. So even if you never actually plug it in, a PHEV is much more fuel-efficient to drive than a conventional petrol or diesel car.