It works in EG because the application scans the HTML, finds all of the referenced images, downloads the images, and fixes the HTML IMG source tags to find them.
For other environments, you'll have to do as @Cynthia_sas says: change the ODS HTML statements to set the image path and the relative reference using the URL= suboption. Then as long as you keep the HTML and image file together in the same relative path, your browser apps should find both.
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