If you do a Google search for "All pedophiles are sex offenders", you get an amusing set of results. A fair number are a quote from Michael Seto, where "not" is prefaced, resulting of course in the opposite meaning.
But there are others that are asserting the positive. Here's one, chosen more or less at random. I believe that one prominent place this quote appeared until a couple years ago was the ATSA website, though for all I know that came from some other earlier source. I don't think it's on the ATSA site any more. The rumor is that some influential people asked them what evidence they had for it, and not having any, they withdrew it. Someone who knows how to use the Wayback Machine might be able to investigate this.
On the face of it, "all pedophiles are sex offenders" is a phenomenally arrogant assertion. A pedophile is by definition someone with a persistent, strong sexual attraction to prepubescent children. There is no requirement that the person be known to scientists or law enforcement or to anybody at all. What evidence could anyone possibly marshal to conclude that all the members of a group -- one defined by their thoughts and not their actions -- are sex offenders if they are undetected by anyone?
One way might be by definitional trickery. In the widely used DSM, to merit a psychiatric diagnosis of pedophilia you need something beyond the basic attraction. A man qualifies if he "has acted on these sexual urges", so he's a sex offender. However, there is an alternative way to earn the diagnosis: "the sexual urges or fantasies cause marked distress or interpersonal difficulty". Surely a person meeting this criterion has not necessarily acted on their urges. If it was certain they had, there would be no need to include this other clause in the definition! (In the new DSM-5, you only need to meet those additional criteria to warrant a diagnosis of "pedophilic disorder". If you lack them, you are just a pedophile without a disorder.)
You don't have to attribute malice to those who said "all pedophiles are sex offenders". You simply have to consider the experience of the clinicians and researchers who study pedophilia. In their personal experience, almost all pedophiles are sex offenders -- the ones who aren't stay hidden. This is true of them and their colleagues and all the people who go to the conferences and write the journal articles. Their impressions reinforce each other.
But one solemn duty of scientists is to recognize the limitations of their research. It's worth extra scrutiny when the claim is that every member of some class of people is guilty of a serious crime. Failure to do so in this case has been damaging to pedophiles who have committed no crime.
The original full quote is roughly, "Not all sex offenders are pedophiles, but all pedophiles are sex offenders". If we qualify it appropriately, it reads, "Among sex offenders, not all are pedophiles. But among pedophiles who are sex offenders, all of them are sex offenders." That sure is profound!
I say that anyone who has a shred of integrity who is running a web site with the statement "All pedophiles are sex offenders" must remove it.
Beyond dismissing the impossibility of celibate pedophiles, is there evidence that we really do exist in substantial numbers? If a situation is rare enough, "innocent until proven guilty" ceases to apply. Even the best criminal justice system is going to make mistakes, and a few innocent people are going to be in prison. But in practical terms we can't just empty the prisons.
In those quotes you found in your google search, the cautious and highly respected sex researcher Michael Seto said we were a population sizable enough to be worthy of consideration, though I don't know his particular reasons for that conclusion.
I will make the case based on what we know about the variety in pedophiles who commit crimes. Consider one of Seto's papers. He found that about half of the men who are convicted of child pornography possession have never abused a child before their crime and never do after (in fact, a mere 2% abuse a child in the 5 years after their release). Now, child pornography possession is a sex crime, but it is quite a different sort of crime. A teenager who sees a tempting link online and clicks it to watch a movie can very well think to himself, "How can watching a movie harm anyone?" Many people argue that it does (a topic for another post), but even they should recognize that it is a different order of harm from deciding to touch sexually a child who is in front of you. My point is that there is no strong linkage. A lot of pedophiles abuse children but do not look at child pornography, and a lot look at child pornography but do not abuse children. Some do both. Surely there is room for another group of pedophiles -- those who do neither. And given that the other three groups are not vastly different in size, one should expect this to be a large group as well.
A little thought suggests that the "neither" group would be even larger if you think that a lot of people in this world say, "I'm not going to break the law" and that this sentiment could be as common in pedophiles as anyone else. They could be further deterred from those particular crimes by the extremely serious criminal penalties and the hatred and ostracism they could expect from family and friends if detected. Many pedophiles-- perhaps even the vast majority? -- might be deterred simply because they have a moral compass, like anybody else.
I have deliberately not cited the evidence that stares me in the face -- all the celibate pedophiles who write to Virtuous Pedophiles and join our group. I refrain because I am sensitive to bias. If researchers made a serious mistake by generalizing from the sex offenders they know to all pedophiles, I would be no better if I confidently proclaimed that almost all pedophiles are celibate based on the ones I know.
Based on the other evidence available, I think a reasonable person has to accept that large numbers of pedophiles are celibate.