Don't see it like that myself, goldcoast.
Look at it this way: The FA's drive to kick racism out of football is just about their biggest project and highest priority at the moment. For them to do nothing about this, and to do nothing very publicly, will be a major embarrassment to them and weaken what support and integrity they may still have. So they are being forced to investigate this fully and take action if needed, simply by their own agenda.
The Met will investigate separately, and having spoken with all parties, they clearly believe that there's a case to answer.
That Chelsea moron abusing Anton on Twitter has probably drawn himself into the police investigation as well, and the chanting by those despicable Chelsea 'fans' last night really isn't helping their cause at all - it puts them clearly against public opinion.
I really don't see, in the light of video evidence, interviews, etc. that this can possibly just go away.