EricF has it right. There is really nothing else it could be.
Not having chess clocks is just clearly worse than having them. (Note: please don’t let that trigger you, and attempt to construct some convoluted argument where no time enforcement is somehow “better”. It’s not, and it’s infeasible. There really must be clocks.)
Given that there are clocks, of course yours must run on your turn and not the opponent’s.
All tournament floor rules MUST inherently involve squishy, less than 100% perfect rules. “Don’t shout loud, racist things at your opponent” is either implicit or explicit in any reasonable set of floor rules for any game. But you can’t precisely define what loud means (decibels? for what duration? etc) or what racist means. But it would be very bad indeed to discard the rule entirely because it can’t be 100% defined. Anything involving the boundary of the game and how humans interact with it or each other must be squishy and that’s fine. Fine relative to not having the rule. More and more effort to define the loudness of what is shouting or what constitutes racism is not really going to help. In the actual situation, a human judge making a judgment call about what is reasonable is totally fine.
It’s exactly the same for if someone is stalling. You can’t say “it’s impossible to precisely define stalling, therefore it’s allowed.” There is no choice but say it’s not allowed, and to let a judge decide. This whole thing is a non-issue because when you’re using chess clocks, the issue is minimized to a microscopic level. If you instead had just ONE clock for the entire match, shared by both players, then it would be a big issue. Frank is taking a long time thinking on his turn, but is it stalling or strategizing? We’ve seen this type of tournament in real life and the squishy rule is so squishy there that it’s pretty hard to deal with. When you reduce the problem to JUST people asking the opponent on their turn what’s going on, you’ve already removed like 99.99% of the problem. The remaining tiny area where you can “cheat” is easily handled by calling a judge and stopping the clocks. I think we could run dozens of tournaments and encounter 0 problems on this. Or maybe 1 at most, which would then be quickly decided by a judge. If it’s more than a few seconds of questioning what’s going on, I’d say stop the clock and call a judge. If it’s more than like two times, that’s suspicious and not usual for tournament play, so a judge should closely watch the match.