"We’re constantly working to detect and stop this type of activity because we don’t want our services to be used to manipulate people." What do they think advertising is?
In other words, "manipulation" is just persuasion that you (or I) don't like.
I'm open to being persuaded otherwise :)
To manipulate is to "Control or influence (a person or situation) cleverly or unscrupulously" (Oxford), or to "control or play upon by artful, unfair, or insidious means especially to one's own advantage" (Merriam-Webster), or to "change by artful or unfair means so as to serve one's purpose" (Merriam-Webster).
Manipulation implies a level of deceit and deception that persuasion does not. They are sufficiently different in meaning that thesaurus.com does not list either as a synonym of the other. Neither does whatever Google is using as its thesaurus source when it decides to answer itself instead of link to a site.
Actually, if we're going to get into this nitpicky level of semantics, none of the words "cleverly, unscrupulously, artful, unfair, insidious" mean "deceit" or "deception".
I'd argue that advertising is pretty inherently unscrupulous, and if it's at all effective, it's clever, artful, and insidious. And you can argue all day long that it's not "especially to one's own advantage" or "to serve one's purpose", but the fact is that if it was really providing a service to customers and not just serving advertisers, that service would be better provided by a neutral third party (such as Consumer Reports, OutdoorGearLab, etc.).
But while we're at it, plenty of advertising is deceitful and deceptive too, so even if that's a prerequisite for being manipulative, advertising is still often manipulative.
"insidious" is actually a synonym of "deceitful" [0].
You could still argue that advertisement is insidious (which I would by and large disagree with), but the previous poster's point about manipulation and persuasion being different still stands.