The phrase "avoided the implication" is correct and usable in written English.
You can use it when discussing a situation where someone has deliberately not acknowledged or addressed a suggestion or inference.
Example: "In his speech, he carefully avoided the implication that the project was failing."
Alternatives: "dodged the suggestion" or "evaded the inference".
But the ECB cannot easily avoid the implication that the perpetual nature of the international cricketing calendar is placing stresses and strains on players to what, this winter at least, has become an intolerable degree.
That may be frustrating for Morgan et al, as it makes it hard for them to avoid the implication that whatever their talents, they are being brought in as electoral window dressing.
Instead of saying that -ing was affixed to sing they preferred to say that sing and -ing co-occurred in a particular pattern or arrangement, thereby avoiding the implication that sing is in some sense prior to or more basic than -ing.
In recent weeks, Mr. Romney's renovation of his $12 million home in the La Jolla section of San Diego has reinforced the fact that he is a wealthy man, forcing his campaign to work harder to avoid the implication that he is out of touch with the concerns of working people.
The title "50 Documentaries to See Before You Die" carefully avoids the implication that these were the best 50 ever made, though Mr. Spurlock appears to be making a larger claim when he says on-screen, "These are the 50 documentaries you need to see before you die".
The 'h' in 'Mohism' is phonetically redundant but conventionally included to avoid the implication that Mohist views are in any way wet.
He calls the theory quasi-pictorial, to avoid the implication that he thinks images are pictures in too literal and implausible a sense.
*Update, 9 October, 11 02 a.m.: This story has been changed to avoid the implication that primarily fathers discuss math with their children.
