I cannot reproduce this fix on my machine. No matter how and where I select the messages, Remove Attachments is disabled.
The difference is clear when you examine the actual mailbox folders and e-mail files in the Finder: for the sent messages, there is no "Attachments" folder next to the "Messages" folder. The "Attachments" folder should be there for messages containing attachments and contain copies of the attachments in folders whose names match the file names of the corresponding e-mail message files (.emlx).
For example, if an e-mail file's name is 143354.emlx and is enclosed in a folder called "Messages" inside the numerical hierarchy that Mail uses internally to organize its files (in the ~/Library/Mail folder), then next to that "Messages" folder there should be an "Attachments" folder containing a folder named "143354" which in turn contains a copy of the extracted attachment (inside yet more numbered folders).
With the sent messages I have, no matter where I put them, the enclosing mailbox folder in the Finder only contains a "Messages" folder with the message file(s). There is no "Attachments" folder with folders with the corresponding names. So somehow Mail has failed to "extract" the attachments and recognize them as such.
The only fix that works for me so far is to export and then reimport the sent messages using the .mbox file format. After that, Mail clearly "sees" the attachments, has the paperclip icon in the message list and has "Attachments" folders inside the mailbox folders for the reimported messages.