It does search the title and the content – but the custom field filters must also match. Filters are also part of the search query, it's their purpose.
I don't know if it's even possible to distinguish between the fields not existing and not matching, as custom field matches are not evaluated one-by-one as it would take much more time for the plugin to process, resulting in really slow responses. ( I know, I tried that solution when designing the plugin)
Currently not matching means, that the number of matches is compared to the overall selected custom field count if the AND logic is selected, or compared to 0 if the OR logic is selected – it's very effective and very fast. If the field does not exist it would return 0 as well, which either means it's not matching or not existing – however in one case the result needs to be discarded, while in the other it needs to be displayed.
Since you are the first one to face this issue, if you can add FTP access as well, I can try to experiment with a possible solution on your server directly. If I can make it work, I would definitely add it to the upcoming version as well.Best,
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