Yes, there are multiple strategies to comply with a buy-Economy restriction while flying F on the corporate dime. For obvious reasons, I won't divulge them all, but here is one to get the gist of how it usually works. It involves UP fares.

You didn't tell us what markets you fly in (domestic, transcontinental, INTL, ...) but on the domestic NYC-HOU market, for example, there is an UP fare with basis YAA00UPY that is a coded as an EU-Economy Unrestricted fare but books into F (fare class C). It has specific features to comply with corporate regulations.

First, most corporate booking systems process these fares as Economy fares because of the EU fare type and that's also how they appear on any official document from UA, except on documents that are only handed to you personally like your boarding pass. Additionally, since you are booked into F right away and aren't upgraded from Y to F, written statements as "I bought an Economy ticket and didn't upgrade my ticket" are technically true and can be backed up. Furthermore, it requires intimate knowledge of fare class codes, which differ for every airline, and is beyond the capabilities of most auditors, to notice what this fare actually is. In this example, the "C" is the only bit that gives it away, and note how conveniently it again says "Economy Fare" to assist in creating reasonable doubt when questioned:


FARE CLS EXPLANATION BOOK CODES
-------- ----------- ----------
YAA00UPY ECONOMY UNR C

It's not up to me, and I believe nor to others on this forum, to judge the ethics of those buying these fares; I'm sure UA has no concerns whatsoever to pocket the money. I also don't have to point out that some companies have cultures that embrace skirting rules in this exact manner, especially when the customer is the one paying for it all. UA offers a fare when it knows there is a market for that fare, and I know for a fact these fares are being bought. There is a parallel YAA0AFEY fare filed for those who want to fly in the back; it's a bit cheaper.