I don’t think Toyota would jeopardize the reliability reputation of the Corolla, especially since the next generation will already be all new. They waited years to bring their CVT and Valvematic in North America.
Since the rumor is from India, it might be related to international market, where Toyota already uses some BMW engines – and vice versa when the new Mini came out. Toyota and BMW are also partners in the development of lithium-ion batteries. So the Supra isn’t an isolated case.
It’s not uncommon, even for major companies, to share the high costs of development as more and more different models are needed to please the market, hence lower volume for each. Like, for instance, the Toyota Aygo/Peugeot 108/Citroen C1, the Mazda2/Yaris sedan or Mazda’s hybrids with Toyota’s technology in Japan. It goes way beyond those old stories of Geo Prizm, Chevy Nova and Toyota Cavalier!
The next NA Corolla will probably be all in-house engineered… except maybe for some XRS type version. The small market for that car didn’t or wouldn’t justify large investments but a bargain BMW engine deal specific to that version would probably have reviewers salivating, beside some enthusiasts, hence doing wonders for marketing with the main versions keeping up a “safer” Corolla image.