"Challenge" might be too strong a word. The survey wasn't too bad and I've no reason to suppose they didn't find damp, and getting them to do the injection would be the easiest move. But. When I look at the area they have indicated as needing it, it looks to me that they have waved their meter around and assumed stuff that frankly doesn't make sense.
Picture shows the situation, entire rear part is "condemned" for rising damp. Not the rest of the party wall. Includes a ramshackle lean to that has may have rising but deffo has falling damp and is clearly going to be removed. There may be damp on the outside wall, for sure, but I reckon any damp on that interior wall is far more likely to be from the shower room, or penetrating from the lean to edge.
Not to scale
dots signify areas marked as having rising damp.
outside wall (end of terrace)
=============================
| |.................................................
| |======================
| |. |. |. |.<<Ramshackle lean to on end
| |. |. |. |.
| |. |. |. |. GARDEN
|
| | . | ....... ...... |.......... |.
|============================= | ==== == | ====|.
| | . | . Bath |.
| | . | . room |. GARDEN
| | . | . |.
==============================================
PARTY WALL (TERRACE) ....................................