I feel strongly about Fort Ann [as the location of Putnam's capture], based on several references. First would be Israel's own recollections, recorded by David Humphreys (page 232) mentioning being "about a mile from old Fort Ann".
The event is also mentioned in Documentary History of New York, vol.4, Rogers journals, and in the Recollections of Thomas Maxwell, a soldier present; Historical Collections of the Essex Institute, vol. 7, page 97.
Putnam had been out with 200 Connecticut men, a company of Regulars and a company of Rogers Rangers. They were in search of a raiding party that had attacked a supply train near Half-way Brook. The total force was approximately 700 men.
Rogers, being in command, split the force. Putnam and his men went toward the South Bay, while Rogers' force went about 12 miles west. After several days, and not discovering the enemy, the forces rejoined and started the march back to Fort Edward.
On the morning of August 8th, Rogers, and a Lt. Irwin of the Light Infantry, decided to shoot at a mark. A French partisan, Marin, was nearby with approximately 400 men, and heard the shots. An ambush was set up near the ruins of the old Fort Ann.
The terrain was described as heavy brush, leading to timber, and wet with heavy dew. The men were moving in a column, with Major Putnam in the lead with the Connecticut men, Capt. D'Ell in the center with the regulars, and Major Rogers in the rear of the column with the rangers.
Putnam was captured, and carried off to Canada. An interesting saying was recorded in reaction to this event. "Rogers always sent, but Putnam led, his men to action."
I would guess that he arrived at Ticonderoga the next day. He mentions being interrogated by General Moncalm, before being sent on to Montreal. It seems likely that he would have passed Crown Point on his way up Lake Champlain, and as likely that he may have been secured to a tree at some time in that journey.
In the biography "Israel Putnam, Pioneer, Ranger, Major General", by William Farrand Livingston, there is a photograph of an ancient tree in the area of Fort Ann, which is claimed to be the one Putnam was tied to.
So, we have the possibility of Israel being secured to a tree near Crown Point. I would not have any difficulty accepting that. His capture though, was almost beyond question, in the Fort Ann area. If I may venture a guess, very near the location of the current Portage restaurant.
Israel Putnam made great contributions to his country during the French and Indian war, just as he did later in the War for Independence.