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Possibly. What matters is how strong the insinuation is.
To sue anyone for defamation of character, you have to establish a few things.
First, you have to establish that the company made a false statement of fact. Now, my concern is the word "insinuation." Some statements can be insinuations, certainly. There are times when an insinuation is strong enough to establish a statement of fact that is false. But you must show a statement, that statement must be in the form of a fact rather than an opinion and the statement must be false.
Second, you have to show that the statement was made to third parties, meaning someone other than you and themselves. This is usually the easiest thing to show.
Third, you have to show damage. Now, in some situations damages are assumed, and a false accusation of being a child molester would allow for damages to be assumed, but assumed damages are not high. They are usually very small in monetary terms, so it would be your burden to show how you have been damaged by the insinuation. You can typically do this through evidence of lost job opportunities, community members that believed the insinuation until you spoke with them about it, to clear the issue up, etc.