How do I explain that an orientation change on an iPad results in elements changing size

I have a website that I've built responsively, it works nicely on a wide variety of screen sizes.

I am working as a subcontractor to a design agency in this case.

There is a navigation menu that is sized to a certain pixel height (its actual height is determined by the height of images within it, their height varies depending on my media queries).

When viewing on an iPad in portrait orientation, everyone is happy with the navigation menu.

When you turn to landscape orientation, the iPad does what its designed to do... it makes the document turn without any distortion of the page. No text reformatting, everything that fit horizontally before still fits, even though there is more horizontal screen real estate.

The design agency is complaining that the navigation menu now appears bigger, however.

My question is more of a general one, I'm not sure how to address this. Some possibilities:

1. The iPad is designed to work this way, it is best not to mess with it... let it do its thing.

2. I should write some additional media queries for this orientation, to resize the navigation menu. This sounds messy, and trying to optimize for a single device may not end with the iPad. I'm also concerned with additional media queries interfering in unintended ways with my existing media queries/screen sizes.

3. There is something fundamentally wrong with the way I'm building the navigation menu in the first place. Maybe the fixed pixel height is the problem, although that could be corrected with additional media queries. I can't see using a percentage to size something like that. The menu is structured fairly complex with a bunch of markup, images, etc.

Would appreciate any advice on this. How would you deal with this when working as a subcontractor?

Thanks!