The below link is the linnk from Official Tax Website of UAE.
If you read the very first line of the law and it says Unofficial Translation tough downloaded from the official site( mof.gov.ae ). The reason is because the original law has been made in Arabic, Now you cannot debate on what you understand from the English Translated law with the one in Arabic as the Arab Countries do not consider english and want to protect their arabic culture. Thats the reason when any invoice is made other than AED, both amounts have to reflect on the invoice. We can show AED amount separately in a line item below.
Also please read Article No. 69 for your reference in the file below. Lot of US & UK Subsidiaries in dubai have a practice of invoicing in USD & Pounds, they also do the same.
These queries will keep arising with everyone who is using it in UAE. As there is not Income tax in UAE, one of the major source for government is fines & penalties which they will do with out considering your explanations to them and the management will have to resort to an other alternative which has inbuilt UAE Invoice Formats for Invoicing purpose and then account for it in Manager. (Instead if we can have a theme configured for manager or a code for UAE Users to paste it as a new theme).
Also, In some legal departments of UAE, official company documents printed in english are not accepted as it is mandatory to translate that document in Arabic and submit.
The effort put is undoubtedly usefull for accountants and book keepers but we really do not want to take chances on clients to have face penalties which is very severe i.e one visit penalty could be some times more than their annual profit and a few cases have also been reported in the news where the company had to be wound up. I know your questions are considerable as I am my self a Chartered Accountant, and we have no option when the government wants it in the manner they prescribe.