This is a fascinating topic with a lot of nuance.
I think some colleges care more than others about obvious signs of privilege. And I think colleges are very much in the know about those summer programs that pretty much any kid with the $$ can do and those that are more selective and provide need-based financial aid. My guess is that the colleges that care weigh them differently.
My kid did two summer programs in the latter category, and we included them on her app. Kid #2 will apply to an engineering camp next summer that also falls in that category.
I agree, however, it is a bit myopic for admissions offices to penalize high pay summer academic or experiential programs when in fact so many top athletes – chess champions – dance standouts – you name it – pay a lot of $$ to get to high level status that attracts admissions attention or, in case of athletes, recruitment. I paid for two years of club volleyball when D was in late middle / early HS – ouch!!