No, that is not accurate. A distinguished point could be anywhere. It's merely how many "zeros" are in a row (consecutive) in a given public key x coord. It shouldn't matter how large the range or private key is. It will just take a lot longer to find a 32 bit DP, in any range. I found several 24 bit DP in that 2^24 range, just no 32 bit DPs. I'm not looking at this to find a key, I am just curious how many trailing or leading 32 bit DPs could be in a range, in particular, the 2^120 range. I thought there might have been a good calculator for it but maybe it is all just mathematical luck, where DPs fall.
"Computing discrete logarithms with the parallelized kangaroo method" by Teske (page 7,
link) states that you can find the number of DPs in a range can be calculated with (2**C)/sqrt[b-a]. C is the number of bits you are using for your DP, and for your problem you can use the full 120-bit range for a and b. So this means 2**32 / 2**(120-1=119) = 2**(32-119) = 2**-87 th of the space are DPs.
To put this in perspective, there are about 27 zeros after the decimal point before the first significant figure.
2^-87? negative 87? Well that's definitely not right. Maybe you meant 2^32 / 2^119 ? Even 2^32 / sqrt(2^119) wouldn't be right. But maybe if you take (2^32 / sqrt(2^119)) and multiply that back by the range = 350,142,318,592,413,374,492,074,613. That would come out to be about .0000054 percent of the 2^119 range.