"less trusted" is correct and usable in written English.
You can use it to express that someone or something is not trusted as much as before. For example, "Since the scandal, the company has become less trusted by the public."
"Big science" and big governments are less trusted now.
The United States itself, however, is less trusted.
In politics you win trust by making others less trusted.
However, both were less trusted than horsemeat-tainted supermarkets Asda and Tesco, according to the survey.
New leaders step forth, but they are inexperienced, and less trusted by the rank-and-file.
Chief executives and accountants have become a despised breed, less trusted even than politicians and journalists.
Loyal units accompany less-trusted ones.
One of Stalin's less-trusted allies, the foreign minister Vyacheslav Molotov, was forced to divorce his wife, then saw her arrested and deported to Kazakhstan.
Daimyo were classed according to their relationships to the shogun as kinsmen (shimpan), hereditary vassals (fudai), and less-trusted allies (tozama; meaning "outsiders").
This extraordinary fact is common across many food and beverage categories where foreign brands selling beautiful and aspirational products are being outsmarted by local brands selling less-trusted and usually inferior alternatives at a greater price, simply by better servicing Chinese consumer needs.
If Russia took the lead on sending in the personnel to secure the weapons sites and begin their destruction, it would avoid the prospect of less-friendly and less-trusted foreign troops (read: Americans) being the ones to take control of the weapons.
