Is EPS still trustworthy if a company can influence EPS via share buy back or share split?
Companies can "manipulate" EPS in a variety of ways. That does not make it untrustworthy, it just means that you can't use it as the sole measure of a company's performance, and have to look for things that do manipulate it, like buybacks, write-offs, etc.
No one measure can be taken in a vacuum. You must look at other metrics to get a complete picture of the company. For example, EPS may be improved via buybacks, but things like cash flow would be negatively affected, which could be a red flag. It also does not affect operations metrics like profit margins, which are more important for looking at future performance.