A couple of things, it is difficult for a parent to know what 'always' does worksheets means - does it mean they never do anything else, that most lessons a worksheet is involved at some point, or that they did a worksheet this lesson. Likewise, it 'is boring' is one of those comments frequently made which is hard to make much sense of. So it is very hard for a parent to know if a teacher is stimulating the class, being boring, giving a range of activities,covering what they should, or covering it to the right standard.
Parents cannot know what is going on in every class. They also are often not in a position (and neither are the children) to judge a lesson. Parents often don't know the wider objectives of a lesson or a group of lessons, or what is required by the course. Children might sometimes find tasks boring or difficult, or whatever, but in itself, these things don't mean the tasks are wrong. They might sometimes find themselves doing lots of the same thing ....again, it isn't necessarily wrong, because there might be a test coming up in that, that needs lots of practise. So, without the full contextual information, it is very difficult for parents to make accurate judgements about lessons - it is one of the difficulties of being a parent.....children spend much of their time at a place, where parents don't know and can't know the full picture of what is going on.
There are times to raise concerns. I would say that they relate to when a parent thinks their child isn't covering the content required (most parents won't be able to judge this) or when the class seems to be regularly poorly behaved to the detriment of learning (again relies of childrens feedback ....listen with caution, but if there is a clear, evidenced consistent message, then pursue it) or when the child seems to not be making good progress (based on reports, parents evenings, feedback in books). It is also worth raising concerns if books are never marked, or teachers are frequently absent - these are concrete things.
However, I don't think it is worth complaining because a parent or child doesn't like the style of teaching - all teachers will be different in their approach, and one child will like one approach and another child not be so keen - it doesn't make the style wrong. It is hard to complain about the range of activities,because again,there is no 'correct' range that should be offered and it is very hard for a parent to know exactly what has happened across a series of lessons anyway. With these kind of things, it has to be left to the judgement of the teacher. As long as progress is being made and there is evidence of that, much of how it is achieved is up to the teacher.
And finally, there maybe more use of textbooks and worksheets in the majority of private schools. Again, I think it is very difficult to draw many conclusions from that - as I said before, neither of these are wrong and can be very useful. Perhaps they are used more. If there are other activities going on too, it is fine and actually spending more time sitting reading and writing might be more beneficial than some of the alternatives.
My understanding of Ofsted at the moment, is that currently it is looking for teachers to show pupils make progress. They are less interested in exactly how that is achieved now, more that it happens. So the idea that every lesson must have 7 different activities to include some kind of physical activity, group activity, IT based activity etc etc is on its way out.....because it is being recognised that things had gone too far in the direction of trying to have a massive range of activities,which actually were not always very useful. Entertaining perhaps, but not actually promoting progress.