Don't use squirrel mail (it suxorz) but I bet it has to do with attached image vs remote included.
There's to ways to add images into email: remotly and directly.
Directly uses the same HTML tags, but the images are attached with the email itself.
Remotely requires making a remote call to load in images.
Spammers have used a method in the past in which they'll implant a remote image href within the email using different image URLs for each email. If that image gets loaded, the spammer knows that's a valid email address and your email is stored and sold off, etc.
Cause of that, email clients no longer, by default, loads remotely included images. This is a feature to protect you and something I'd suggest not to change.
As for the specific problem with squirrel mail, sorry can't help you there. I don't use it. I hate it and I refuse to use it. I forward all my email to gmail and use their interface for email.