Are the MOEs for two mutually exclusive & completely exhaustive percentages equal?

Hello,

A Monday puzzle here:

I am using table B08201 to look at vehicle availability.  The first estimate is total households, and the second estimate is households with no vehicle.  Thanks to the worked examples in the ACS handbooks, I'm able to compute the percentage & associated MOE of households with no vehicle, no problem.

But now I need to calculate the percentage and corresponding MOE of households with a vehicle. The percentage itself is easy. But the MOE of this has me thinking, should the MOE for the percent of households with a vehicle be the same as the one I computed for percent of households with no vehicle? It's still a percentage with the 1st and 2nd estimate of the table. I'm computing it the long way and comparing. It is extremely close for all states, and I'm not sure if these slight differences are being introduced because I'm approximating the MOE for the count of households with a vehicle vs. using the official MOE for the count of households with no vehicle (B08201_002M).

These two percentages (HHs w/ a vehicle & HH w/ no a vehicle) are MECE - Mutually Exclusive, Completely Exhaustive. Meaning, percent of HHs w/ a vehicle = 100 - percent of HHs w/ no vehicle. Would the MOEs of these percentages be the same?