Thanks all.
The Home person that each tree is built around is the one who took the DNA test ie my husband, my mum and my dad, and the test is linked to them. I haven't taken a test and don't appear in any of the trees - the test taker is the person I built the tree around.
ThruLines shows up on their accounts, and on mine which manages them, but in both their accounts and mine my parents ancestors show as potentials rather than definite. As far as I can see it doesn't stop ThruLines working as it should, so maybe it's just something I need to live with!
When you are looking at a tree the sidebar that shows the icons for which view to have the tree in, the house icon, zoom in/out, and the rotation icons etc, at the bottom is a DNA icon and if clicked it opens up a panel called DNA Discoveries.
ThruLines Icons is off and greyed out in my parents trees but is on for my husbands.
Possible DNA Matches is on and
Connected DNA Matches is on.
What it seems to do is add a little DNA symbol to his direct ancestors in the tree.
It might be that this setting being off and my parents showing only potential ancestors when looking in the ThruLines section is completely unrelated, but it's the only thing I can see which might explain the difference!

Mind you it took me forever to be able to see the ThruLines in the first place because when the link to accept the sharing of their trees came through it didn't actually say something useful like "click here to confirm" only a "Check it out" button - so I didn't click it because I already knew what was in the tree so didn't need to 'check it out'! Turned out that was the acceptance link!!
