Batteries connected both in series and in parallel
"Some sources" are correct - but only in certain circumstances. If you are driving a fixed resistance, connecting two batteries in series will, in fact, double the current. Well, approximately. It won't be an exact doubling, since batteries have a volt/amp curve which produces less voltage for more current. For very low currents and some high-current battery chemistries, two batteries in series may come very close to twice the current.

For high currents, such as a level which will discharge the battery in 10 hours or less, you can count on a noticeably smaller capacity when the current is increased.

Conversely, to your specific situation, you've done the calculations correctly, and 7 minutes/14 minutes is about right. However, since each battery string is providing half the current when in parallel, you might reasonably expect greater run time. Like maybe 15 minutes instead of 14.

Your figure, on the other hand, makes no sense at all, and I have no idea where you got the idea.