The engines don’t have to go back to China - there are country level overhaul facilities for it. The Russians offered Turkey exactly this with the KA-52 Erdogan variant - Pakistan has has very high availability rate with F-16s but also with JF-17s as well - it did suffer what you are talking about with the F-6 in the early years but once the rebuild factory got put into place the things were fairly acceptable.
The issue isn’t (apart from the fact this is likely a fake at best or facetious at worst article ) but that you are right the J-10 offers NOTHING to Turkey it already doesn’t have access to and more importantly the F-16V is the lowest lift to integrate into the TuAF.
Forget the sanctions potential, diplomatic fracas or otherwise - the J-10 is a flat choice from a plain capabilities and systems addition. There is the TFX , the Kizelma and deep F-16 knowledge base - what possibly could the J-10 offer in that.
@Bilal Khan (Quwa) is right - the EF is the logical choice when it comes to adding an interim upgrade to the TuAF for its needs which it can both absorb and sustain easily.