Any professional interviewing for a role will have several years of experience under his belt. A recruiter cannot decide on the basis of a 15-30 minute phone call whether the candidate will be a good hire for the next few years. All you can gauge are communication skills, interest, availability, background, CV points and so on. If you find a mismatch between the CV and candidate's responses, then flag the candidate. Else he must be interviewed in detail in subsequent rounds.
There is a common cognitive bias called the Dunning-Kruger effect. It allows people with limited ability to overestimate their skills at a task. If you have interviewers in your panel who claim to assess candidates within 10 minutes or so, then you may have this issue. It is important to re-train such panelists.
A screening interview is never a decision point in a selection process. You can miss out on some great prospects if you are not careful.
Note: Phone screening interviews are different from an interview conducted over the phone.You can look at hundreds of examples of feedback on PM phone interviews on Glassdoor.com. Here is one example of a Google Product Manager phone interview. Here is an example from Amazon India.