The full quote from episode 90: "In 97 AD, a Chinese embassy was sent west to try to make contact with 'The Kingdom of the Daqin', which is what the Han called Rome. But apparently, they were stopped short in Mesopotamia after the Parthians explained that the difficult crossing to Rome would take another two years at least. This bald-faced lie was meant to keep the two poles of the lucrative trade routes - which Parthia controlled - from ever meeting and working out a way to bypass the Parthian middleman."
Is there evidence that it was formal state policy of the Parthians to keep China and Rome from forming more cohesive diplomatic relations?
The story largely comes from a wonderful source called the Hou Han Shu, which is a Chinese history of the later Han Dynasty. In particular, it comes from a section called the Weilue which I understand translates to "Western regions". In particular particular, it comes from a description within it of a journey by an envoy named Gan Ying, who was an attempted ambassador to Rome in 97 CE. The account:
In the ninth yongyuan year [97 CE], during the reign of Emperor He, the Protector General Ban Chao sent Gan Ying to Da Qin (the Roman Empire). He reached Tiaozhi (Characene and Susiana) next to a large sea. He wanted to cross it, but the sailors of the western frontier of Anxi (Parthia) said to him: “The ocean is huge. Those making the round trip can do it in three months if the winds are favourable. However, if you encounter winds that delay you, it can take two years. That is why all the men who go by sea take stores for three years. The vast ocean urges men to think of their country, and get homesick, and some of them die.”
When (Gan) Ying heard this, he gave up his plan.
Given that "Tiaozhi" is on the Persian Gulf we can sense a bit of fibbing going on here, and this has certainly been taken up by many scholars to show that the Persians had an active policy of denying Chinese access to Rome. Is this reasonable? Of course not, the idea is ridiculous. The Parthians did not exist as some sort of nebulous historical villain trying to forever separate East and West. That doesn't keep many reasonable people from claiming otherwise, but given the very brisk Roman trade with India there is no reason to think the Parthians had any policy of trying to isolate Rome, even if they were able, or that they would cared about a Chinese envoy one way or another.
This is contra Raoul MacLaughlin's Rome and the Distant east and largely following Gary Young's Rome's Trade with the East.