Axes sizing in MATLAB can be a bit tricky sometimes. You are correct to suspect the paper sizing properties as one part of the problem. Another is the automatic margins MATLAB calculates. Fortunately, there are settable axes properties that allow you to circumvent these margins. You can reset the margins to be just big enough for axis labels using a combination of the Position and TightInset properties which are explained here. Try this:
>> h = figure;
>> axes;
>> set(h, 'InvertHardcopy', 'off');
>> saveas(h, 'WithMargins.pdf');
and you'll get a PDF that looks like:
but now do this:
>> tightInset = get(gca, 'TightInset');
>> position(1) = tightInset(1);
>> position(2) = tightInset(2);
>> position(3) = 1 - tightInset(1) - tightInset(3);
>> position(4) = 1 - tightInset(2) - tightInset(4);
>> set(gca, 'Position', position);
>> saveas(h, 'WithoutMargins.pdf');
and you'll get:
