Hi Alexander,
In Ireland, the situation is almost as you hypothesise, as, while Tree Pipit isn't on the list of species considered by the Irish Rare Birds Committee (it was, prior to 1994), it is merely a scarce visitor to our shores, never having been proven to breed or suspected of it, either. Meadow Pipit, on the other hand, despite recent declines and being Red listed, is a common bird, found in every county, and more widespread on migration. Accordingly, we have to be careful in claiming Tree Pipit here, and I can recall, in my younger days, going to Great Saltee every spring and getting excited by this or that pipit, which seemed to have fine flank streaking, which would invariably turn out to be Meadow Pipits.
I think that, while the flank differences are usually useful, this is a species pair where concentrating too much on any one feature can be a recipe for disaster, and, as I am sure you yourself would agree, using a range of features gives more confidence in the identification. The subject birds have, among other features, long hind claws, orangeish legs (pinker on Tree), longer thinner bills, no hint of the ear covert spots shown by many Trees and so on. The head pattern and bill thickness are subtle features, but they do add up to give a distinctive expression to (most?) Tree Pipits that is lacking on these birds.
Regards,
Harry