It is standard practice for the body parts to be Text then HTML.

I think the RFC explains the situation fairly well http://www.w3.org/Protocols/rfc1341/7_2_Multipart.html

To quote

As a very simple example, the following multipart message has two parts, both of them plain text, one of them explicitly typed and one of them implicitly typed:

    From: Nathaniel Borenstein <nsb@bellcore.com> 
    To:  Ned Freed <ned@innosoft.com> 
    Subject: Sample message 
    MIME-Version: 1.0 
    Content-type: multipart/mixed; boundary="simple 
    boundary" 

    This is the preamble.  It is to be ignored, though it 
    is a handy place for mail composers to include an 
    explanatory note to non-MIME compliant readers. 
    --simple boundary 

    This is implicitly typed plain ASCII text. 
    It does NOT end with a linebreak. 
    --simple boundary 
    Content-type: text/plain; charset=us-ascii 

    This is explicitly typed plain ASCII text. 
    It DOES end with a linebreak. 

    --simple boundary-- 
    This is the epilogue.  It is also to be ignored.

The use of a Content-Type of multipart in a body part within another multipart entity is explicitly allowed. In such cases, for obvious reasons, care must be taken to ensure that each nested multipart entity must use a different boundary delimiter. See Appendix C for an example of nested multipart entities.

The use of the multipart Content-Type with only a single body part may be useful in certain contexts, and is explicitly permitted.

Thank you for the feedback. The most relevant quote from the RFC seems to be:

In general, user agents that compose multipart/alternative entities should place the body parts in increasing order of preference, that is, with the preferred format last.

I understand that Thunderbird follows the RFC where other readers appear to make their own choices to which part to display. Thank you for pointing me in the right direction. Now I can go back to the sender and try to get them to "fix" their message generator.