Here's the definition from Merriam-Webster online:
"transitive verb 1 a : to introduce (as an idea) gradually or in a subtle, indirect, or covert way <insinuate doubts into a trusting mind>
b : to impart or suggest in an artful or indirect way
: imply <I resent what you're
insinuating>
2 : to introduce (as oneself) by stealthy, smooth, or artful means"
bluegiraffe, although your example doesn't square with the dictionary definition, it does seem to work with the etymology: "Etymology: Latin
insinuatus, past participle of
insinuare, from
in- +
sinuare to bend, curve, from
sinus curve". Perhaps you were subconsciously picking up on the Latin root here, or thinking of the word "sinuous" which means "having a wavy or serpentine form".