Strictly speaking he's telling the truth.

First off:

imply
transitive verb
1. To involve by logical necessity; entail: Life implies growth and death.
2. To express or indicate indirectly: His tone implied disapproval. See Synonyms at suggest. See Usage Note at infer.
3. Obsolete To entangle.
[The Free Dictionary]

(This'll make more sense shortly. Trust me.)

Carrying GOP talking points a bit too far:

Rep. Steve Austria: FDR caused the Great Depression.
In a new interview with the Columbus Dispatch, Rep. Steve Austria (R-OH) joined in:

“When (President Franklin) Roosevelt did this, he put our country into a Great Depression,” Austria said. “He tried to borrow and spend, he tried to use the Keynesian approach, and our country ended up in a Great Depression. That’s just history.”
[emphasis included in source (Think Progress)]

More than a few folks corrected him: The Depression started in 1929; FDR took office in 1933. It's hard to posit cause-effect relationship when the "effect" precedes the supposed "cause" (tho' there may be such relationships in the realm of quantum physics). So Rep. Austria backed off:

"I did not mean to imply in any way that President Roosevelt was responsible for putting us into the Depression..."

Finally - here's where the introductory definiton of "imply" becomes relevant.

In fact, Rep. Austria did not IMPLY that FDR had caused the Depression. He directly stated this.
No involvement of logical necessity, no indirect expression or indication. Just a simple, straight-forward, direct statement.
It's not even necessary to subject Rep. Austria's words to complicated exegesis - even a 5th-grader could grasp their direct, unambiguous meaning:

"When (President Franklin) Roosevelt did this, he put our country into a Great Depression."

So... on some level he's telling the truth when he recants by saying he never meant to imply anything...

This was fun.