The first time I loaded Fallout 4 after installing the latest patch the VDSG entry on the loading screen told me about the Lone Wanderer perk and said it applies when travelling without a companion or dog.
It's widely documented that in fact you do still get the perk when travelling with Dogmeat.
I've never seen this particular entry before, or never noticed it anyway. Did it always say that, even though actually it does work when traveling with Dogmeat, or did they "fix" the perk in the patch?
If it always said that, then it's just always been wrong, and the perk probably still applies when travelling with Dogmeat.
If it didn't always say that, and the text was updated for Patch 1.3, then that suggests to me that they also fixed the perk so that it no longer applies when travelling with Dogmeat (even though this isn't mentioned in the patch release notes).