Your friend would be right, except that he missed some key information about specific vs general. The Lich's paralyzing touch attack is a secondary natural weapon, but only because it's specifically noted as such:
A lich has a touch attack that it can use once per round as a natural
weapon. A lich fighting without weapons uses its natural weapons (if
it has any) in addition to its touch attack (which is treated as a
primary natural weapon that replaces one claw or slam attack, if the
creature has any). A lich armed with a weapon uses its weapons
normally, and can use its touch attack as a secondary natural weapon.
The Vitalist's Steal Health ability, on the other hand, says:
As a touch attack, the vitalist may deal a number of hit points in
damage to the target equal to his vitalist level + his Wisdom modifier
and heal an equal amount of damage.
Steal Health is a Supernatural ability, and this is what the rules have to say about those:
Using a supernatural ability is usually a standard action (unless
defined otherwise by the ability's description). Its use cannot be
disrupted, does not require concentration, and does not provoke
attacks of opportunity.
Unless the ability defines a different action (which Steal Health doesn't, and Lich's touch does), it defaults to a standard action.
The Lamia's Wisdom Drain ability appears to be of a different sort of ability. It says:
A lamia drains 1d4 points of Wisdom each time it hits with its melee
... and lists a Touch as an attack taken within its full attack action. The wisdom drain ability is a rider effect, much like Poison or Disease, rather than a Supernatural ability used "as a touch attack."
Amusingly, I think this would mean that a Lamia Lich would both paralyze and drain wisdom if it poked someone, and that a Lamia Vitalist could steal health in addition to sapping their target's will.
Naturally, the DM might read things differently. It's entirely possible to interpret "as a touch attack" as "this is an Attack action that is also a touch attack" rather than "this is a touch attack", but I feel that it's unfounded in the RAW. My suggestion is to ask your DM, after pointing out various examples of things that are and are not listed as used as part of Attack actions.