Utilize your financial knowledge, give your answer or opinion to the input question or subject . Answer format is not limited.

What could be the harm in sharing my American Express statements online?
If someone gains access to these data, he could use social engineering approach to impersonate you - i.e. call the American Express and ask tell he he is you and he lost the access to the account and he needs the access to be reset and sent to certain email, and if they doubt it's you he would send them the statement data, even on company letterhead (which he would be able to fake since he has the data from the statements, and AE has no idea how the authentic letterhead looks like). He could also do the opposite trick - like calling your assistant or even yourself and saying something like "I'm from American Express, calling about the transaction at this-and-this date and this-and-this time, this amount, please confirm you are {your name} and your address is {your address}, I need to confirm something" - which would make it appear as he is really from AE since he knows all these details - and then ask you some detail he's missing "for security" - like your birth date or last digits of SSID or anything like that - and then use these details to impersonate you to AE.  So putting all this info together where it can be accessed by strangers does have risks. It may not work out if both you and AE personnel are vigilant and follow instructions to the letter, but we know it not always so.