If you go to the section on natural healing on pg. 105 of the PHB, it says:
"Characters heal naturally at the rate of 1 hit point per day of rest. Rest is defined as low activity - nothing more strenuous than riding a horse or traveling from one place to another.
If the character has complete bed rest (doing nothing for an entire day), he can regain 3 hit points for the day."
Then go to the PHB on pg. 59 and read the healing proficiency:
"If a wounded character remains under the care of someone with the healing proficiency, that character can recover lost hit points at the rate of 1 per day even when traveling or engaging in non-strenuous activity. If the character gets complete rest, he can recover 2 hit points per day while under such care. Only characters with both healing and herbalism proficiencies can help others recover at the rate of 3 hit points per day of rest."
WTF?



Ok, let's summarize:
Natural Healing (ie no help from someone with healing proficiency)
Recover 1 hp/day of non-strenuous activity, 3hp/day of bed rest
Healing With Healing Proficiency
Recover 1 hp/day of non-strenuous activity, 2hp/day of bed rest
So basically you recover 1 hp/day while riding your horse home whether or not someone with the healing proficiency tends your wounds! Why bother to have someone bandage you up? I guess to humor the poor cleric who thinks he can make a difference?

Laying in bed with no one to minister to your wounds allows you to heal 3 hp/day, but if someone with the healing proficiency tends to your wounds, you only heal 2hp/day? WTF?

And it's worse...
If you lay in bed alone getting rest, you heal 3 hp/day. If the poor sucker who took both the healing and herbalism proficiencies tends to your wounds...nothing changes! You still heal just 3 hp/day! I mean, why bother?
I've always added that healing onto the natural healing. In other words, if you're doing nothing more strenuous than riding your horse home, you naturally heal 1 hp per day, but if someone with the healing proficiency tends to your wounds, that means you heal 2 hp/day total.
If you get bed rest, you heal 3 hp/day naturally, and an additional 2 hp/day from the ministrations of a healer (or 3 additional if tended to by someone with both healing and herbalism).
Otherwise, why bother with those proficiencies? I think they dropped the ball on that and confused themselves (TSR) when they wrote that.