Can PTAS $\epsilon$ parameter be dependent on the algorithm input?
If $A$ is an algorithm whose running time is $O(1/\epsilon)$, then if you substitute $\epsilon = 1/n$, its running time will be $O(n)$. This is a property of the particular algorithm $A$ rather than of polynomial time approximation schemes. We have absolutely no guarantee on the running time of a PTAS when $\epsilon$ is subconstant (i.e., when $\epsilon = o(1)$).
The running time of algorithms tends to depend on the input length (though it's not always the case), so I'm not convinced that $A$ really has running time $O(1/\epsilon)$.