It's true that intravenous insulin causes a potassium shift into the cells (which is why we use it to bring down a high K+).
i'm not sure why that would get labelled as a 'false' low, though - the potassium level's still low, because that intracellular K+ isn't available.
Whenever we have patients in DKA they have a hydration line, a glucose line (once the BSL drops below 15 mmol/L), an actrapid (insulin) infusion and a potassium infusion
, which is titrated to their serum K+: 10mmol/hr if it's over 5.5, 20mmol/hr if it's under 5. They have four-hourly electrolyte monitoring to keep an eye on the K+ and everything else, and 6/24 gases if they came in acidotic.
Sorry, I know I've burbled on - put it down to night duty! Hope this helps