Definitely true. The age of a domain name shouldn't be the only determining factor.
But a domain name that was registered last month and is selling web hosting plans will definitely come across as more shady than a domain name that has been around for 20 years.
Now does that mean that the 1 month old domain is not legitimate? No. But does it mean that the 20 year old domain is not legitimate? Probably not, since it has a higher chance of having a higher reputation.
But you may have been in the hosting industry for the last 30 years and know it inside out as an employee, but made redundant, so you decide to go it along and purchase a domain and get a site template.
anyone looking you up will just see a new business with a new domain, does that mean the company cannot be trusted.
Everyone has to start somewhere.