Hmmm...been giving this some thought. I was thinking that a parent led activity was like some sort of class for 30 mins, like now we are going to learn throw-catch for 30 mins straight. Which there is no chance of and which sounds hugely demanding for both parent and child to keep that going for 30 mins. We can throw catch for about 2 mins (or less) before it turns into kick, roll, run, ignore ball, jump on sofa, run to kitchen screaming, play tig, start counting to 10 for hide and seek. There is no 'class' or specific parent led activity.
BUT now that I've thought a bit more I've changed my mind. I think parent led just means parent involved rather than 'led' and in that sense 30 mins is almost nothing. And 1hour free play across a day is almost nothing too (where as one hour solid might be too tiring, I know my DS can only do 30 mins at the play park. Just about an hour at a soft play centre but split by a break for drinks, snacks and a sit down).
What I realised is that some LOs might spend much of the day restrained in various ways eg highchair for meals, car seat into town, buggy all around town, cot for naps, car seat to the supermarket, trolly around the supermarket, even trips to smaller shops or paying bills etc might be restrained by hand holding so the LO gets little chance in the day to play at all. In that case it might be very important for the parent to focus on encouraging active play by not putting the TV on at all where as my DS is very rarely restrained by anything (high chair for meals, cot for naps, car seat very short trip to play group, approx half or less of our supermarket shopping time, he walks and carries heavy groceries to the trolly until he gets tired then has a sit in the trolly for a snack and rest then out again to help with the rest of the shopping) so he is physically active most of his awake time, if I put the TV on and he needs a rest he sits down for a few mins, otherwise he is climbing and balancing on his little chair whilst he watches or he's doing yoga or dancing with the cartoon characters (and often me too!).
Sorry, this thread was really just me thinking out loud in the end. I did have a sudden bout of worry that I wasn't doing my job properly but I feel happy about it now.