John, I am no legal expert, but people in this country can and do sue over just about anything. Donald Trump has spent a lot of his own money and he claims that Ted Cruz who he believes to be an ineligible candidate has already caused irreparable harm to his candidacy and reputation through what he characterizes as lies. He has made numerous warnings that he is going to sue if Ted does not cease and desist.
So he has:
1. Something to adjudicate.
2. He can demonstrate injury and has standing.
3. This is not a political question... it is a constitutional question.
Will he ultimately win... with a 5 to 4 conservative majority on the Supreme Court... probably not. With a deadlocked court and a panel of liberal judges from the 9th Circuit hearing the obligatory appeal... who knows? From my experience the judges will go with their political inclinations and construct legal justifications. This will most likely mean 2 judges to 1 judge ruling against Cruz and the Supreme Court deadlocked.
I am something of an expert, but that's not the issue. The old saw you are quoting is one that says anyone can sue anyone for anything at any time. True enough, if all you mean is that anyone can FILE a lawsuit against anyone at any time.
Getting a court to put the case on the docket is another matter entirely.
This particular case won't make it onto the docket of any Federal court, for the reasons I have given and more.