This claim is based on conversations with 4 consultants at these firms in North American and Europe. 

I've heard two explanations for this:  

1. These firms under-hired earlier in the pandemic.
2. High churn. A large part of the compensation for these roles are the travel perks, and most consultants are still not traveling for work. I heard that one European office lost 40% of its staff this year.

80,000 Hours recommends investigating other paths before entering consulting, but if it makes sense in your situation now could be a good time to apply. 

There was recently a sequence written on management consulting if you're interested in learning more.