Having not been convicted of a crime (with the assistance of one of the world's largest legal budgets) is not the usual measure of being the sort of respected and trusted person you'd want at the helm of your corporation.
The man is unquestionably toxic - it's entirely possible the entire company is toxic.
Board members and shareholders aren't responsible or particularly concerned with innocence or guilt, but are very concerned with trust and respect that customers (or potential-investors/business-partners/governments) have in their company's leadership.
They're not deciding whether to put him in jail or not, but board members are legally obligated to determine whether or not he's adding or detracting from shareholder value.
Even if every single accusation against him and the culture he's built is false - the public perception needs addressing. Perhaps "remove" is the wrong wording, but if you're an insider/board member who thinks every single accusation and report is false - you'd at least have to seriously consider asking Travis to publicly "recuse" himself while the investigations are under way - without that anything coming out of the investigation is going to be about as believable as the Police Union guy announcing "We've investigated the matter and cleared ourselves of any wrongdoing!".
The man is unquestionably toxic - it's entirely possible the entire company is toxic.