It isn't equivalent. Grooming isn't simply being nice and complimenting and trying to get close. It's also about isolating the target and eliminating their ability to perceive their escape options.

That's not okay, to put it mildly.

Did you actually read the abstract dbaupp just linked to?

All sex offenders had received in-hospital treatment for six months to one year and were mostly non-defensive about various forms of enticement, exploitation or entrapment, including threats of harm, used to elicit eroticized responses from female children. A sizable number of incest (61%) and pedophilic offenders (58%) confided they felt powerful and in control. One third of men in each group relied on some element of gratuitous violence (e.g., pushing, grabbing, shoving or spanking) to force compliance from unwilling children.

I'd call that a pretty healthy falsification of "trust."

How can they be wrong about consenting?

Manipulation. Children are prone to manipulation by figures they trust. So they have belief-in-consent, not actual consent.

From the abstract of this paper:

The findings point to the slow, but deliberate, 'grooming process' used by men who erotically prefer children as sex partners over mature adults

Edit: Nvm, there's a reason we generally think these threads are a bad idea.

Short answer: if a child thinks they're consenting, they're likely enough to be wrong (with great enough consequences) that the expected value is negative. Much more importantly: if an adult thinks a child is consenting, the adult is likely to be wrong (they'll have a hard time between telling the difference between actual consent and consent that is feigned out of fear).

Is consent hypothetically possible? Yes. But you're running on corrupted hardware and the expected value will usually be negative.

some generous interpretation of "very likely", or something else?

What I mean, roughly, is that if you raised in Western or Eastern Europe, any of the Americas, the Middle East, Asia or Africa, then you probably grew up under some abusive mode of childrearing (childrearing is much more advanced in the Nordic countries). The socializing mode is the most popular these days, although intrusive parenting can also be fairly common too depending on the region.

Try The History of Child Abuse if you're interested.

Does your support for the first hinge on a strict definition of abuse,

Read up on the basic archetypal childrearing modes (infanticidal, abandoning, ambivalent, intrusive, socializing, and helping) for a better idea of what I mean by abuse. You can find information about them in the above link, and even the wikipedia article isn't too bad.

I don't know if I actually believe this, but I've heard reports that cause me to assign a non-neglible probability on the chance that sexual relations with between children and adults aren't necessarily as harmful as they may seem. For instance, see the Rind et al. report:

"Child Sexual Abuse does not cause intense harm on a pervasive basis regardless of gender." Simplified, Rind et al. (1998) found that 3 out of every 100 individuals in a CSA population had clinically significant problems (compared to 2 out of every 100 in a general population).

Rind et al. contended that the degree of psychological damage was based on whether the child describes the encounter as consensual or not.

Similarly, I've heard second-hand accounts about people who report that they actually had loving relationships with pedophiles as kids. That didn't traumatize them, but the follow-up "psychological care", where the psychiatrists automatically assumed that the experience must have been horrible, did.

It would seem reasonable, on the face of it. There's no automatic reason for why we should assume sexual relations with children must automatically be harmful and unpleasant to the kids, if not for the cached thought of all sexual relations being abuse. And in the current political climate, just about nobody will have the courage to voice such an opinion in public, so studies such as these should carry extra weight.