I can imply or insinuate that someone is dishonest- imply can go either way, so, yes:
Imply- positive or negative
Insinuate- negative
Therefore, the mistaken usage is likely to be with 'insinuate' rather than 'imply'. Another common mistake is to confuse 'imply' and 'infer'- people use 'infer' wrongly- the speaker implies and the listener infers. This is a common error amongst native speakers too.
