There's quite a lot of twaddle in that article, so I would not regard it as an authoritative source of info. Bear in mind that the author works for Groove Tubes, ie a company that sells (expensive) valves.
As stated, a 12AT7 has a lower gain than a 12AX7, and can source more current than a 12AX7.
The main effect of using a 12AT7 instead of a 12AX7 in a long-tailed pair (LTP) PI is to reduce the gain. Unless the circuit has been optimized for 12AT7s, ie the plate load resistors have been reduced in value from the typical 100K (Fender used 47k in the later Silverfaced amps), then additional current sourcing capability will be negligible.
Bear in mind that most amps inject negative feedback into the bottom of the LTP, so any reduction in gain of the LTP will also reduce the feedback factor.
Also, assuming that the balance of the LTP has been optimized for a 12AX7 (and many haven't), then using a 12AT7 will unbalance the outputs; whether this is good or bad
I've had good results with 12AT7s in the LTP, but not so much in pre-amps. 12AT7 experience heavy grid currents when the input is overdriven, and I think this is why they don't work as well in pre-amps.