I'm surprised someone tried to estimate that this is one-in-1300 years event when we don't know how they form, have no data on them, don't know much about those waves.
If there are 500 measuring stations, then every year some one of them is going to experience a once-in-500-years event. We just never notice the other 499, and cherry-pick the one outlier after it already happened. (Yeah, there can be correlation between station measurements; obviously I'm speaking in generalities.)
Not really. You got it exactly backwards. The return period of an event is determined based on all recorded events. This does not mean that massive events that took place in the past didn't existed if no record was kept. Consequently, massive events are underrepresented both in magnitude and in frequency, and consequently estimates of their return period tend to be larger.
Think of it this way: the concept of the return period of an event (i.e., this is a one in X year's event) is determined based on the average time between similar events.
The buoy was in for at most a handful of years, and catches a 1-in-1300 year event in that one location?
The first thought on that should not be "what incredible luck!", but "is there something special about this location, or is that 1-in-1300 estimate off?".
We know a surprising amount about their mechanics due to replication in the lab [1][2]. We don't have lots of observational evidence to support the lab effects accurately replicating the ocean, but I don't think we've generally seen evidence for lab surface water materially differing from ocean surface water.
[1] https://en.wikipedia.org/wiki/Rogue_wave
[2] https://openresearch-repository.anu.edu.au/bitstream/1885/70...