But - in doing so, he has no right to pilfer his former employer's trade secrets and either use or disclose them in the new position. An employee can use his general skills and expertise freely in any position, as these are not tied to misuse of confidential, proprietary information. The tension lies between your right to work freely using your skills and restrictions placed on you to the extent you learn confidential things in your old position.
Thus, the general answer to your question is that, yes, you can work for another company doing a payment service even if you have worked for PayPal, but you can't use or disclose trade secrets from your former employer in your subsequent job. Do gray areas come up in such situations? All the time. Usually, they don't lead to lawsuits. In extreme cases, they do; in abusive cases, they also do, though these are not justified (i.e., where a former employer wants to chase and punish an employee just for having left employment). In the vast majority of cases in California, nothing happens and the former employee freely moves on - at times immediately, at other times after some delay. (Results may vary in other states where the law may be different and particularly where non-competes are enforced).
The federal Espionage Act of 1996 provides: "Whoever, with intent to convert a trade secret, that is related to or included in a product that is produced for . . . interstate . . . commerce, to the economic benefit of anyone other than the owner thereof, and intending or knowing that the offense will, injure any owner of that trade secret, knowingly . . . steals, or without authorization appropriates, takes, carries away, or conceals, or by fraud, artifice, or deception obtains such information . . . shall . . . be fined under this title [i.e., up to $5 million] or imprisoned not more than 10 years, or both."
That said, it would be highly unusual for the authorities to attempt to prove a criminal violation in this sort of case. I think the overwhelming odds are that it will be treated as a purely civil case.