When I'm reading, my eyes movement scanning the page must be in sync with my perception and reading or the words. I'm not reading words that my eyes scanned half a second ago. Otherwise I'd be "reading" the last word of a line when my eyes are already at the start of the next line?
To take another example, when I'm cooking, my hands movement are certainly in real-time sync with what is happening at that very moment in the real world, otherwise I'd have few remaining fingers after cutting a few vegetables.
I'm no claiming that perception is instantaneous, but clearly we do many activities successfully that implicitly require perceptions to be near real-time.
If the theory is correct but the timing difference is small enough that these objection go away, then I feel the theory is just a change of nomenclature. What they call memory is just the perception delay.