It may be related to this:
For the equation: y'' +3y' - 7y = e^{t}. Using the method of undetermined coefficients, you would guess that $Ae^t$ is a particular solution of the equation. But this wouldn't work if $Ae^t$ were a solution to the homogeneous equation. Then, you'd guess $Ate^t$ for a particular solution (assuming that wasn't a solution to the homogeneous equation, in which case you'd try $t^2e^t$). To check if $Ae^t$ is a solution to the homogeneous equation, you'd check if $r=1$ is a solution to the c.e..
In your case, I think, the reason for mentioning that $r=1$ is not a solution of the c.e., is because that tells you that the guess for your particular solution should contain a term $Ae^t$ (the guess contains other terms because you have $t^4e^t$ on the right hand side).