Some conjugation fun with “insinuar”

I’m writing an essay where I want to say: “They both now have new lovers, but it is hinted [implied] that the protagonists were…”

I tried writing it as: “Los dos tuvieron amantes nuevos, pero es insinuado que los dos protagonistas serían…”

And my prof’s handwriting looks like they want it corrected it to: “…pero se insinuía que…”

What’s tripping me up is, as far as I can tell, “insinuía” isn’t a word. Any ideas on how I can correct this sentence (or what my prof meant)? I’m more concerned with it’s being technically correct, but any advice on how to make something sound more natural is appreciated too. ¡Mil gracias!

submitted by /u/Oganesson-294
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