Correlation between nominal bond returns and growth
When growth and inflation are primarily driven by aggregate demand, nominal bond returns tend to be negatively correlated with growth


Actually, the above sentence is the explicited version of what you have in mind, i.e. the links between nominal (vs real) returns, (demand-driven) inflation and growth.


  when growth and inflation are primarily driven by aggregate supply, nominal bond returns tend to be positively correlated with growth.


The point is that "supply-driven inflation" is the broad way of saying "weak or no inflation" or even "deflation" (avoided since politically undesirable). Put differently, when growth and inflation are primarily driven by aggregate supply, nominal bond returns tend to be ... real and thus to be positively correlated with growth. Indeed, the traditional (neoclassical) explanation is that non-weak real rates stimulate savings which in turn stimulates technical progress and ultimately, economic growth.


All that being said, the passage you quote is curiously phrased.. and the key words appear to be "tend to be".