The example sentence: "That thing seems me very suspicious" is nonsensical. There is no indication of what "me" is doing in the sentence structure. The addition of "to" defines what "me" is doing. Without the "to", the reader does not know if the "me" applies to the "That thing seems" part of the phrase, or the "very suspicious" part of the phrase, so the intended meaning is unclear. Adding "to" makes it crystal clear that "me" is referring to "That thing seems".
So, the thought can be defined. "That thing seems very suspicious." has meaning. The thought is clear. "That thing seems to me very suspicious." Now the original phrase is modified so that the thought is clear, AND we know that the speaker is limiting the observed truth to their own interpretation. It moves the simple statement from the realm of absolute assertion, into a statement that recognizes personal viewpoint as having an important impact on the viewing.