Yes, they had to pay Qualcomm for their LTE patents, but that didn't mean they had to use Qualcomm SoCs.

Other devices (e.g. Galaxy Nexus, Droid Bionic, HTC One X+) married Qualcomm LTE radios with non-Qualcomm SoCs. Even Samsung did this for a few devices (e.g. Galaxy Note and Note 2 LTE, a few S2 and S3 variants), but, until this year, that was a small and shrinking portion of their lineup.

Qualcomm's past engineering success was a big part of the reason why. Samsung/ARM's engineering failures (e.g. big.LITTLE and cache coherency issues with the original Exynos Octa) were the another part of the reason, but I don't think that changes the overall picture.