The reason why TSMC might invest in Intel is to get a piece of the US domestic market that it's now somewhat unable to reach. That could constitute domestic manufacturing behind a tariff scheme (if these tariffs hold), it could constitute ITAR manufacturing that TSMC is excluded by law from doing, but can hold a minority stake in such a company, it could constitute taking a share of products that it otherwise can't access - Intel CPUs, etc. This is why automakers are constantly taking stakes in and partnering with their competitors, because when you have what is effectively a cartel structure with a small number of players carving up a fixed market, you want to take stakes in all of those players because they all constitute insurance policies against your market.
As to the reporting, what TSMC wants to do and what the Govt of Taiwan wants to do in this extremely fraught moment around Trumps policies may well be very different and they are certainly working together to navigate this. If a TSMC investment in Intel fabs would be a win for TSMC and for Intel and for Trump, the Taiwanese govt may ask them to deny any interest in that in order to put heat on Trump at a time when the country wants these tariffs removed. You can't invest anything in rumors in this kind of environment because they can all be true and contradictory at the same time.