Erm, no they don't. I personally collect all of the rewards from it. I have a nice fat account of AmEx MRs (and plenty of hotel and airline points) thanks to all of my corporate card spend.
edit: I have no idea why this is being downvoted. Do you want me to show you a screenshot of my MR account as proof, or something? AmEx corporate cards absolutely give the card rewards to the employee, not the company.
See https://millionmilesecrets.com/news/you-can-earn-american-ex...
From your link
>However, if your company has blocked the American Express Membership Rewards program, you will NOT be able to enroll your corporate cards.
Also
>To earn American Express Membership Rewards points, you have to pay $90 to enroll your American Express Green Corporate card or American Express Gold Corporate card.
So only worth it for people who know they will be big spenders and who won't leave the company for a long time. For someone who travels only once a year (like me) totally not worth it. I'd rather collect the ~$30 cash back on my 2.5% cash back card.
The company collects all the rewards for the spend but you take on all of the risk of repayment. If you used your personal card you'd collect the rewards.
Using personal cards and being reimbursed is a nice perk for many.