Yes, but the point is that flipping a single bit can change a value dramatically. While using 64 bit ints for example programs are likely using a limited range

Yes, but the point is that flipping a single bit can change a value dramatically. While using 64 bit ints for example programs are likely using a limited range of values and flipping a bit in say the middle of the int will change the value by plus or minus 4294967296. Not many programs will handle this gracefully.