Is this spread really mean-reverting?

You regress a daily pairs spread on its own lag (with an intercept) over $T = 250$ days and get $\hat\phi = 0.97$ with standard error $0.015$. A colleague says: "The t-statistic for $\phi = 1$ is $-2.0$, below $-1.645$, so we reject the random walk at 5% and the spread mean-reverts with a half-life of about 23 days." What is wrong with this argument?