Syndication can hurt your original’s ranking, but only when it is uncontrolled, when the syndicated copy outranks your version because it sits on a stronger partner site with no canonical pointing back to you. The risk is real in that scenario, and it largely disappears when the syndication is managed, with partners using a canonical tag or clear attribution to your original. The pivot is whether the syndication is controlled. Set up properly, syndication reaches new audiences without costing you your ranking; set up carelessly, it can hand your traffic to the site you handed your content to.
The mechanism behind the harm is duplicate content choosing a winner. When the same article exists on two sites and there is no signal telling Google which is the source, Google decides for itself which version best serves the query, and it tends to favor the more authoritative domain. If your partner outweighs you in authority and nothing points back to your original, their copy can win the ranking, leaving your version buried beneath the one you supplied. That is the uncontrolled case, and it is exactly how syndication earns its reputation for backfiring.
The control that defends against this is built into the agreement, not bolted on afterward. A rel=canonical on the syndicated copy pointing to your original tells Google your version is the source and consolidates the ranking signal back to you. Where a canonical is not possible, a clear attribution link to the original on the partner’s page helps establish provenance and can pass some value back. With either in place, you get the reach of syndication while keeping your original as the version that ranks. So neither blanket claim is true: syndication is not always safe, and it does not always hurt, the outcome depends entirely on whether you controlled it.
Before you syndicate anything, make the control a condition of the deal. Require that the partner place a canonical tag pointing to your original, or at minimum a clear attribution link back to it, and confirm it is actually in place after publication. Negotiate that up front, and syndication extends your reach instead of quietly undercutting the page you started with.