A bit of background:
The "free" bikeability courses are funded by central goverment to the tune of £40 per child trained. To get this funding the instructors have to teach to the National Standard which bears the Bikeability branding, and they have to be registered with and trained by an Instructor Training Organisation (ITO). The teaching is constantly audited and spot checks are carried out by representatives from Steer Davies Gleave on behalf of the DfT. If, during an inspection, it is felt that the Instructors are not working in line with the National Standard the possibility is there for SDG to recommend that funding to the Bikeability Provider (the organisation the instructor is working for) can be suspended. This covers not only the actual training of the young people, but the risk assessment of the instructor regarding bike suitability, training areas etc.
These "clowns" as you put it, are primarily responsible for the safety of the young people in their care (on road ratios of 1:6). As you put it "the tyres were starting to reach the end of their service life" so you knew they were a potential safety issue, but still allowed your daughter to go on a training course that would invovle cycling in traffic. So if that makes them "clowns" for looking out for your daughter's safety, that must make you a "muppet" for not doing the same.
Part of the course is aimed at getting the young people to recognise faults or potential issues with their own bikes, so to spot a tyre needs replacing, but to do nothing about it would be a tad hypocritical of the instructor wouldn't it.
@reglard Suffolk Council may be the Bikeability Provider, but they are NOT allowed to tell the instructors how to run courses or what content to teach. Only the Bikeability Provider's ITO is allowed to do that, and according to the July 2014 lists, Suffolk Council is not an ITO. If the Council is found to be in breach of that, it will lose all Bikeability funding.
And yes, before you ask, I am one of those "clowns". I am also an instructor trainer for an ITO, so I also train those "clowns".