Those who spoke with Haaretz reporter Anschel Pfeffer have two aims. The first is to protect the reputation of the IDF. The second is to signal political actors like the Ministry of Foreign Affairs that the Tzahal is pretty darn good, but to expect miracles is a risky policy.
On the record, the IDF claims that it "has ways of dealing with large scale protests" and would likely never admit anything to the contrary. Israel's security, and Israeli public confidence, requires that the IDF maintain this dominant posture. Off the record, the article betrays some well-founded concern that mass non-violent protest may be out of the IDF's ability to handle without creating casualties. A challenge for any army, the IDF is nervous that it will bear the blame for when things go wrong in the wake of the next round of mass protests. By leaking such concerns off the record, the IDF can preempt accusations that it was unprepared for a mass protest.
The second important point is that these apprehensions demonstrate that the IDF is grounded in reality and has a sense of its actual capabilities. Other actors in the Israeli government are not so in touch. In light of the upcoming Gaza flotilla, The IDF has raised its media profile recently in order to create familiarity with its narrative and cast of characters. The relationship this media presence creates with the global public will help lend credibility to the IDF's version of events in the wake of a second flotilla raid. With regards to protests, the IDF publicized its lessons learned from Nakba day and implemented them well during the Naksa Day protests.
But in both cases, the IDF and not the Israeli Foreign Ministry or Prime Minister's Office is defining the narrative. Depending on one's perspective, the IDF is either undermining the authority of the government or picking up after it's many mishaps. When ministers in the Israeli government claim their own government's claims are unsubstantiated, this betrays a serious lack of confidence in the government's ability to exercise a nuanced and pragmatic policy towards the Palestinians. While the IDF takes stock of the threats ahead, the government is playing diplomatic catch-up, needlessly toughening conditions on Palestinian prisoners, and putting vague and unnecessary preconditions on discussions with the Palestinian Authority. None of these steps does anything to delegitimize non-violent protests over the Israeli occupation, or stop a flotilla of so-called activists from embarrassing Israel over its blockade on Gaza.
The IDF should be expected to follow the conventions of war, preserve human life whenever possible, and maintain the security of the State of Israel. However, it should not be expected to single-handedly address the myriad political crises which the current administration's myopic policies have created. Non-violent Palestinian protests are a political reaction for which the government bears primary responsibility. Rather than hide behind the IDF's ability to control reaction to consistently spurned policies, the government would be much more effectively advancing Israeli security by shifting the policies themselves.