JessM, my mum's behaviour was exactly like your grandmother's. No walk, or visit to any country park or garden was complete without mum snipping cuttings of any plant she fancied. She also nipped out with a bucket and shovel whenever the rag and bone man came down the road.
We didn't have germoline (luxury!), mum made a poultice of sugar and soap if we had a cut that went sceptic. I confess to doing the same thing when my children were small.
Grannie always had the family baby on her knee, and as soon as the baby was ready for solids, would chew bits of food, to feed to the baby. Amazing that so many of us are still here to tell the tale, given we roamed the countryside unsupervised, and lived in smoke filled homes.