I think you are seeing a more extreme position than they were taking.
It's not that there isn't value in having friendly relationships with your colleagues no matter their gender. The issue comes up in comparing the value of a specific relationship with the potential costs of it (or attempting to create it).
Right or wrong, befriending a male colleague has virtually zero risk. The chances of anything happening to severely damage your career or social standing are essentially nil. Even in a severe situation, there isn't much you can do to cause a problem without acting in a pretty horrible way that's also documented. There just isn't much you can do there to really provoke a highly emotional reaction or scare HR.
The same cannot be said of attempting a relationship with a woman. People are very sensitive about sexual harassment and HR wants absolutely nothing to do with it. The exact lines for sexual harassment are necessarily a bit blurry. Even if they existed, continually just barely not crossing them would seem like harassment to me.
Is the friendly relationship with a woman coworker so much more valuable than a man that it is worth taking on additional risk? I don't think so.
I don't intend to have a particularly strong relationship with all my coworkers and I imagine most people are the same. This means I get to be choosy about which ones I engage in this way. The risk-reward ratio just doesn't seem favorable to engaging women in this way.
Now, personally speaking I have slightly more female friends than male friends, unless we're counting people I might talk to once every few years. My oldest friend, by far, is female. I would never suggest men should not be friends with women. That's insane. I'm just not sure what the incentives are for me to try to specifically befriend female coworkers.