Current return path when using an AC coupled transimpedance amplifier

Is a current return path a good (or reasonable) design practice with an AC-coupled transimpedance amplifier?

Horowitz & Hill states that "you must provide a return to ground for the (very small) input current" and an article at analog.com on common design errors highlights this as a common design error.

It is not clear to me if a current return path is also required with an ac-coupled transimpedance amplifier. When I look at Horowitz & Hill, the ac-coupled transimpedance amplifier section of the circuit shown in Figure 8.87 does not have a current return path after the blocking capacitor. It could have been omitted for clarity because the figure shows the ac-coupled as an optional configuration.

FWIW, I am not designing a circuit. I am trying to understand some unusual behavior in some equipment and my working theory is that the blocking capacitor is building up a charge over time (as indicated in the analog.com article).

I have included a circuit diagram (revised to show the recommended resistor from the lower plate of C1 to ground).

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