"Unfounded speculation" refers to making guesses or assumptions about something without any solid evidence or logical reasoning to support it. It means that the speculation is baseless and not grounded in reality. Full definition
You may think paleo based climate sensitivity values add useful information, but for me they are eye - rollingly uncertain, and filled with unfounded speculation about conditions which can't be confirmed.... (judithcurry.com)
Aregbesola frowned at what he described as unfounded speculations ov er the party's choice of Husain, saying neither him nor any member of the party had done Adeleke's family any harm. (nigeriapoliticsonline.com)
The drama generated by the disease has led to much unfounded speculation about farmers dumping dogs, but while this has been going on, much larger numbers of Border Collies have been re-homed by people who took them on as pets, and this is documented fact. (bordercollierescue.org)