I’m making a website and would like to add their logos to a “happy clients” section. I won't be including any of the work I did for them, just their logos.
Yes, but it's all in how you phrase it.
When I was with [Marketing Company X], I assisted clients such as Nike, Reebok, Adidas, Puma.
I've worked with Nike, Reebok, Adidas, Puma.
While it's a fine line, and most won't really care. There is a different connotation if you were employed by someone and worked with clients compared to directly working with them.
It's not like there's a legal reason you need to disclose the employer you were with. It's more of a "don't lose the client's trust" type of thing. If they think you were directly working with Nike, then a month later they find out you were an employee of a company which worked with Nike, they can feel betrayed. But if that is disclosed upfront, there's no risk of betrayal feelings.
However, hyperbole can be viable tool for some. So it's really more you're call. I, personally, don't like to pretend I'm something I'm not. It avoids sticky situations later if the truth is uncovered.