Another 18 percent said that was “somewhat important,” while less than 2 percent said it was “not very” or “not at all” important.

Read: It's time to rebrand 'true fiduciary'

Respondents to the survey who ranked that fiduciary status as very important covered a range of participant groups: investors who use target-date funds (76 percent), investors not currently working with an advisor but interested in doing so (73 percent), those with assets between $100,000 and $500,000 (72 percent), and investors who already work with an advisor (70 percent).

A lot of participants still aren’t working with an advisor, however, and the barriers to doing so are pretty substantial: 46 percent cited affordability, while 36 percent said they felt they didn’t have enough assets to get an advisor’s attention.

Twenty-six percent weren’t sure how an advisor could help them, and 23 percent were do-it-yourselfers, preferring to go it alone.

And while people have been interested in robo-advisors, with 60 percent being interested in online advisory services, more were interested in online services that also provided access to real live human beings (68 percent).

Participants were interested in getting answers to questions such as the appropriate savings rate that would allow them to meet retirement goals; turning 401(k)s and other retirement accounts into reliable retirement income; figuring out their overall financial wellness; how to assess their personal risk tolerance; and how to optimize Social Security claiming strategies.

Financial Engines, for its part, looks to be seizing the opportunity presented by people’s interest in having a real person to talk to, and has increased access to live investment advisors.

While participants in its managed accounts already have access to the company’s advisors, now participants who are enrolled directly in plans and are not part of the managed account program will be able to access live advice via phone.