You are not paranoid, it's indeed very bad to use drives from the same batches, for a simple reason :
- Same drives, built the same way, from the same components, used the same way, are likely to fail at a same time.
I've been working for years at a data recovery company, and i've seen amounts of RAID array with several drives failing at the same time (within array rebuild time), usually all those with consecutive or very close serial numbers (I recall a sad customer who had a RAID of 5 drives, 3 of them having the magnetic substrate wiped out from the platter...)
I'm not sure if you are talking about a RAID system here, but if so, I advice against mixing drives from different makers, as you'll lose performance due to different seek times and data transfer rate, and as Farseeker stated, you're likely to have size issues with raid.
To splay the failure date of these drives, you should turn to different resellers, since it's unlikely they'll have the same batch of drive.
You can also "burn" those coming from the same batch : use heavily one drive alone one week, add another drive and use them both heavily another week, add a third drive and use them three heavily ... For 16 drives it is a bit inconvenient, so you should evaluate the risks of the drives failing in the same period to set the burning time.