You talk as if a paper being peer reviewed makes what it says truth.
You may believe that peer review means that someone goes trough all the data, calculations and algorithms used, making sure all is correct.
That isn't how it works.
That is why in many cases after a paper being published (which meant it passed peer review) errors are detected and papers have to be changed and sometimes are withdrawn.
Then there are papers that are created, peer reviewed and published, that exist solely to contest another peer reviewed paper.
Additionally many times the data (and more important the raw data) and algorithms/calculations aren't provided with claims that it is IP.
How can one review something if the data and the algorithms aren't present?
And if the ocean heat content was increasing and the ice that exists on land was melting due to increased temperatures, the sea level should be increasing at an accelerated level in the recent decades.
http://www.sciencedirect.com/science/article/pii/S0921818113002750
"Abstract
We use 1277 tide gauge records since 1807 to provide an improved global sea level reconstruction and analyse the evolution of sea level trend and acceleration. In particular we use new data from the polar regions and remote islands to improve data coverage and extend the reconstruction to 2009. There is a good agreement between the rate of sea level rise (3.2 ± 0.4 mm·yr− 1) calculated from satellite altimetry and the rate of 3.1 ± 0.6 mm·yr− 1 from tide gauge based reconstruction for the overlapping time period (19932009).
The new reconstruction suggests a linear trend of 1.9 ± 0.3 mm·yr− 1 during the 20th century, with 1.8 ± 0.5 mm·yr− 1 since 1970. Regional linear trends for 14 ocean basins since 1970 show the fastest sea level rise for the Antarctica (4.1 ± 0.8 mm·yr− 1) and Arctic (3.6 ± 0.3 mm·yr− 1). Choice of GIA correction is critical in the trends for the local and regional sea levels, introducing up to 8 mm·yr− 1 uncertainties for individual tide gauge records, up to 2 mm·yr− 1 for regional curves and up to 0.30.6 mm·yr− 1 in global sea level reconstruction. We calculate an acceleration of 0.02 ± 0.01 mm·yr− 2 in global sea level (18072009). In comparison the steric component of sea level shows an acceleration of 0.006 mm·yr− 2 and mass loss of glaciers accelerates at 0.003 mm·yr− 2 over 200 year long time series."
Bold is mine.