Okay. Let’s try to see what is the amount of information (I) produced by a stem cell that differentiates into a naive B cell producing an antibody with a given specificity S.
We have (I)=-log2( P ), with P being the probability that the stem cell gives rise to a naive B cell producing an antibody with specificity S.
Given that estimates of the theoretical diversity of the human naive B cell repertoire range from 10^12 to 10^18, it can be said that P range from 10^-12 to 10^-18 and, as a result, that (I) range from 40 to 60 bits. Note that this range for (I) is an overestimation, for I assume here that there exists only a single antibody with specificity S in the whole repertoire, which in most cases is obviously false. Note also that (I) should not be confused with FI, for FI is related to the improbability to generate the antibody randomly from an unrelated state, which is not at all the case with the process of VDJ recombination.
Bottom line: the maximum amount of information that the process of VDJ recombination is able to produce range from 40 to 60 bits, far, far away from the 500 bits required to draw a design inference. IOW, neither this process nor the process of somatic hypermutation invalidate ID.