This is a somewhat unknown territory because there is no direct reaction between phosphate (PO4-) and active chlorine (HOCl/OCl-). However, there is evidence that even in clean and clear swimming pools, high phosphate levels tend to cause sporadic issues with chlorine demand. The go-to answer is always that the phosphates are feeding algae, causing the algae to reproduce faster and use more chlorine. That is certainly the Occam's Razor answer but I don't always buy it. There have been people that have posted and they swear their pools are clean to TFP standards (and I give them the benefit of the doubt and believe them) but the SWG doesn't keep up. Then they remove phosphates and the cell is working again. Sanitized water doesn't have much, if any, algae in it and so I have always wondered about side reactions inside the SWG cell that could cause issues. I'm still in the "thinking it through" phase and haven't yet come up with solid chemical evidence so I'm not going to say much more than that. I'll keep noodling away at it but don't expect any brilliant light-bulbs to go off any time soon.
That said, if DSP wants you to remove phosphates as a condition of them playing nice with you, then do it. It's cheap enough and easy enough to do and, if you remove the phosphates and the cell still isn't working, then DSP owes you a replacement and they've run out of at least one excuse in their "avoid the warranty" arsenal...