China and Soviet Union were fighting for primacy in communist world, they both needed Vietnam for that
First we need to notice that Sino-Soviet split started before Vietnam war, and long before 1969. Without going into too much details, conflict was mostly ideological but some national interest were also involved. Both sides criticized each other, but that did not prevent them for supporting same side in Vietnam war (i.e. North Vietnam) . Overall, Soviet aid trough years fluctuated but it was not affected substantially by events in 1969. Chinese help peeked in 1967, and was somewhat reduced after that, but didn't stop completely. Both sides were trying to pull Vietnam in their own sphere of influence, and Soviets seemingly had upper hand in the end. Nevertheless, China did not out of blue switch sides in Vietnam because that would harm their prestige in communist and pro-communist countries around the world . In fact they were giving aid right until the end of the war.
As for near war situation, this is somewhat over-exaggerated. There was one serious battalion-regimental level conflict over Zhenbao (Damansky) Island in March. Russian Wikipedia has substantial details. Second one was platoon-company sized near Tielieketi/ Lake Zhalanashkol in August, and again Russian wiki has details. Soviet society was semi-closed at that time, so they were able to suppress details about the losses somewhat, although in 1970 when situation eased somewhat they acknowledged losses and gave medals to those killed and wounded. Chinese suppressed information even more, to this day they only acknowledge 68 Chinese soldiers KIA, real figure probably closer to couple hundred. Anyway, on September 14, 1969 both sided met and agreed to back off a bit. Conflict remained frozen until 1990's when border disputes were settled. Throughout whole period (March-September) diplomatic relations were not broken, and neither was rail or air traffic. This may seem strange in our time, but in those days informations in communist countries were tightly controlled, and disseminated mostly trough newspapers and radio . Therefore population of both countries, especially China, did not know much about what was happening.
As a final note, 1969 US public was already sick an tired of Vietnam war . Nixon started Vietnamization and Operation Rolling Thunder already ended. Soviet shipping was free to move cargo directly to Vietnam, without going over Chinese territory. This would also affect potential Chinese overland blockade (and make it partially useless), and probably made China abandon this as an option.