I have always thought in 標準語 those two words should always be 頭高, as corroborated by several authoritative sources including NHK. But I have very occasionally heard other pitch patterns. This one sounds clearly to me like 平板: かれしが{LHHH}. Why is that? Also, what about 彼女? Is it ever realized as 平板?
An additional question is: how are they pronounced in 関西弁? Because I talk with people from 関西 a lot and they switch back and forth between dialects, which makes it hard for me to be certain if their pronunciation is standard.