It's not the companies that are proud of it per se. Not directly at least. The people who are proud of it are the ones directly involved, typically lower downs in HR or the public facing department.
The message gets translated when coming from the top down or when going into the public. It turns into something to the effect of how inclusive and diverse the company is. The higher ups especially turn a blind eye (or are in complete denial) of the actual practices which happen.
A handful of low level employees deliberately violating company policy is very far from your original statement of"several large companies in my area which, due to diversity pressure, blatantly discriminate"
Not just violating company policy; violating federal law.
There is little congruence between C-level and workers at a large company. It doesn't take many levels of separation for that to occur.
In this case, the discrepancy lies between people at the top saying that they value diversity and inclusion, then people who doing the hiring acting on that message based on their interpretation of it.
Companies do a LOT of things that are sketchy at best and overtly illegal at worst. The amount of time since the last public fiasco is generally a good indicator of how fast and loose they play (even more for companies which have never had a negative public incident).
The message gets translated when coming from the top down or when going into the public. It turns into something to the effect of how inclusive and diverse the company is. The higher ups especially turn a blind eye (or are in complete denial) of the actual practices which happen.