I used the word 'unchanged' to indicate that the sea level in the Marshall Islands is unchanged. It is currently approximately where it was 23 years ago. This is a pretty common usage. If a stock trades up and down all day and ends where it started, you will hear people say 'it ended the day unchanged'. Or 'unch'. Sea levels in the Marshall Islands are currently 'unch'. Over a period of 23 years.
And make no mistake, I acknowledge the worldwide trend in sea level is upwards, the evidence of one tidal gauge doesn't trump the evidence of thousands of tidal gauges. And it has been upwards of course this entire interglacial.
Now, your example of a linear trend superimposed on a sinusoid is a good one. So let me say this, it's a pretty fucking pathetic linear trend if, 23 years later, the bottom of the sinusoid is still overlapping the starting point. The noise in the measurement, and the seasonality, is greater than the supposed trend. It's worth considering for example the coastline of Manhattan 100 years ago. This trend you speak of is utterly insignificant on a human timescale. We can literally grow land faster should we so desire. For example, consider the fact that many Pacific islands are growing due to sediment accumulation (http://www.bbc.co.uk/news/10222679), so weak is this trend. And yet, we're expected to sit here and swallow the premise of this article, the concept of 'climate refugees' and compensation...