There are only two things which can authorize you to log ANY time in the right seat of an aircraft (in a US/FAA context):

1. The aircraft is type-certificated by the FAA for two pilots.

OR

2. The aircraft is being operated under an FAA OPSPEC or other FAA authorization/requirement which requires two pilots.

Insurance requirements are not regulatory, even though certain states may require insurance.

This is an easy fix though. Make a single log book entry with today's date and subtract out all of the time logged in error. Make a brief note stating what this is for and the date range of the erroneous logbook entries...this will make it easy for future interviewers to see what was going on.

Also remove the time from any online apps you submitted. If anyone asks why your total time dropped, you have a good explanation basically an honest mistake which probably was caused by some scumbag lying to you when you were an entry-level pilot. Much better to fix it yourself than get called out on it later.

If by some chance you already took a checkride based on this time (ie ATP), you have more work ahead of you. You'll need to contact the FAA and explain the situation and they will probably make you re-take the checkride (don't exercise the privileges in the meantime). Talk to a lawyer before you call the FAA, but I'm pretty sure they'll consider this a mistake, not fraud. At least if you catch it before they do.