I’d say that people can argue that the opposite is true. We’re less connected with the people around us and we share things which are more trivial and matter very little. The ease by which we can share has enabled that.
Further I'd say that it holds true for me and my family. It's not uncommon for me to share more via Facebook in a night with my wife than in person. We can sit on the couch and ask each other if we saw our latest update, without talking about anything serious.
This is absolutely our own fault. We choose our level of interaction, but Facebook (and Twitter) masks trivial sharing as deep relationship.
Now I've made very good friends online, and I don't think we should be giving that up. We do need to be way more honest with ourselves. 99% of what we share online is trivial, and that trivial sharing can easily hurt our real life relationships because we feel like we share all day.