The issue is how much the care will cost in the future.
I'm having trouble seeing the relevance. Maybe you missed this from post #10
Odd twist is that her LTCi is an "indemnity" policy which pays a flat dollar amount if she is in a facility, regardless of the amount she is spending out of pocket.
Suppose her policy would pay $7,000 per month today. She can either use the insurance to pay (most) of this month's care, or she can take the money out of savings. Suppose her savings will grow at 2% per year, the LTCi benefit grows at 5%.
If she starts insurance benefits today, she'll keep $7,000 in savings. Six years from now when her LTCi benefits run out, that $7,000 will have grown to $7,883.
If she defers filing for insurance for at least a month, she will pay for the NH with $7,000 from savings. She won't have that $7,883 six years from now. But, her policy benefit will still be payable, and will have grown to $9,381.
In that case, she is $1,498 better off by not using her LTCi for this month.
(That is my other sister's reasoning. Since the LTCi benefit grows faster than here conservatively invested assets, she's ahead by spending down assets now and letting the LTCi benefits grow.)
Notice that the cost of care doesn't matter. It could be $6,500 or $7,500 today, it could be $7,000 or $8,500 or $10,000 six years from now. I don't need to know which is right to see that she'll be $1,498 better off
if she lives long enough to exhaust her LTCi benefit.