My assessment is this:

1) There is no DHS regulation/law/rule that says you can't use an F lav if you're in E.

2) There is no FAA regulation/law/rule that says you can't use an F lav if you're in E.

3) Airlines may have a policy of not WANTING passengers in E coming up and using F lavs.

4) Air crews SOMETIMES enforce the airline policy.

5) Air crews USUALLY make it part of their pre-flight or post-takeoff announcement that passengers SHOULD/MUST/PRETTY PLEASE use the lavs in their ticketed cabin.

6) In this announcement, the air crew will FREQUENTLY say it's UNITED's/AMERICAN's/etc security policy. SOMETIMES they say it's FAA. SOMETIMES they say TSA. I personally have never heard then say DHS, but it wouldn't surprise me if they do.

7) It is inaccurate to say that it's a GOVERNMENT policy/rule/law, but they say it anyways. They do it anyways, since it has more weight behind it if passengers think the government is the source of it and will enforce it. It is WRONG of them to do it, but they do it anyway. Most passengers believe them. If you know it's WRONG, there's not much you can do about it. Maybe use the F lav and not flush?

As a practical matter, on a widebody, it's not that big of a deal. There are usually plenty of lavs in the middle and rear of the plane. On a narrowbody, however, it's pretty common for E passengers in the first few rows to use the F lav, especially if the drink carts are in the aisle or if there's a long line in the back. Whether I'm sitting in F or E+ on United, I have rarely seen an FA make a stink about someone coming up to use the lav under those circumstances. If the rear lavs and the aisle are clear, there's a good chance that the first class FA will ask someone coming up to use the one in the back. This may be before or after that passenger uses the lav.

Personally, if I'm in E+ and can't make it to the back lavs, I'll use the one in the front but actually tell the FA "sorry for using your lav, there's a line/beverage cart in the back". I don't do it that often, but when I do, it's usually an "ok" response.

I don't think it has a thing to do with actual security - as far too many "security policies" don't. It's to keep the forward lavs cleared as best as possible for F and C passengers, and to cut down on the foot traffic through the F and C cabins.