I'm actually impressed that those six words conveyed so much meaning and it came through as well as it did. But, the rest of the words in the rule also matter.
Never forget the "After they have had a reasonable amount of time" part. Were they doing something other than trying to arrive at and determine the lie? The clock started when they
should have been able to get there.
It is reasonable for someone to walk rather than run, go out of their way to cross at the bridge, take the least-thorny path through the woods, etc.
Note that the four points begin with After, After, After, and During. "After" means that once the clock starts, it does not reset. (Except if you are no longer Next, like if the previous thrower decides to re-throw.)
Nothing you can do as the next player gets you a new 30 seconds.
However, if you are in a situation where you may need to decide whether to go to a drop zone, or whether to abandon the throw, the 30 seconds
does not start until you've had enough time to figure that out (and make the walk). That would include enough time to try out your lie to see if it's worse than the alternative. Even then, once the group thinks you've had enough time, the 30 seconds starts whether you have made the choice (and the walk) or not.
Obviously, falsely pretending you might be thinking about moving the lie would be unsportsmanlike. Better to get a harmless time warning than a DQ.
"During" means that the clock runs while the playing area is clear. Or, to put it another way, if the playing area is not clear the clock freezes. It does not reset. When the crowd moves out of the way, you get
whatever remains of your 30 seconds.
These are all designed to make the rule work in the way players want to enforce it.
You should never need to feel rushed, but only waste time when it's NOT your turn to throw.
The group knows when you are wasting time; there are no technicalities you can invoke to legally waste time.