The BSA has safety guidelines. They require that each time a unit does any activity other than meeting at their normal meeting place, the unit must file a Tour Permit. That Tour Permit includes a signature space where one of the leaders going on the trip certifies that they have a copy of the BSA's "Guide to Safe Scouiting" (available at their Service Centers and on their web site for free) and have read it. The unit is obliged to conform to the policies in the Guide (a.k.a. 'G2SS'), and are told that one of the conditions to having protection from the BSA's liability insurance is that the activity where the liability comes from is conducted in conformance with the G2SS. This is doubtless a condition imposed by the insurance company - they won't pay unless the incident occurred while the activity complied with the G2SS. It's not the BSA making the call here.
They are just as responsible for putting people in leadership positions.
Actually, no. They are not. Leaders for Packs, Troops, Crews, etc. are recruited and chosen by the unit sponsor, not by the BSA. It is the reponsibility of the sponsor to know who the people are that they are choosing to be leaders for the children of the community. If they don't know them and have a good judgement of their character and ability, they're not supposed to sign them up. The BSA does run a nation-wide legal check to see if there are any protection orders or felony convictions, DUI's, child endangerment or other such things on the person's records (using the applicant's Social Security number and driver's licence), but that's all they can do. It's the sponsor's job to hire, supervise, and fire leaders.
If those people were ignoring the rules of the BSA, shouldn't the BSA have done something about it?
How would the BSA know? The BSA has about 4000 professional staff. All the other members are either Scouts or volunteer Scouters (Scouters being Cubmasters, Den Leaders, etc.). How would the BSA be aware that a Pack has put some kids onto a float that had no railings or safety restraints, especially at the very time of the parade itself?
The BSA provides program materials, training materials, guidelines, etc. to community organizations so that they can conduct the Scouting program. The BSA itself does not conduct that program and has no way of doing so. It's up to the community organization to see that it's run properly. If someone tells the local BSA organization that they know that a particular organization is ignoring policies, then the BSA can and does investigate and do what it can to correct the situation, including pulling the sponsor's unit charters. But there's no way for it to observe all the activities of the tens of thousands of sponsoring organizations and units in real time, nor is there any way for it to conduct investigations, outside of what's available in legal records, of every single individual that volunteers for Scouting. That's the sponsors' job; that's what they agree to when they sign a charter agreement and the Adult Application.