Fact, but with caveats.
Internet wisdom states that no two amps of the same type sound the same. That is true, but the reasons are far more simple than many would have you believe. Tales abound of esoteric effects such as wire dress, transformer orientation, phase of the moon, etc. And while these do have some effect, it is arguably inconsequential relative to the single biggest source of deviation: tone control tolerance.
I've spent the last ten years modeling tube amps and the number one thing I see is that tone controls are very inconsistent devices. First of all the tolerance of the control is typically 20%. That's plus or minus 20% so 40% total. A 100K pot can be as low as 80K or as high as 120K. This is contrast to the tolerance of a typical passive component which is 5% or less (usually much less IME).
Secondly the resistance at the midpoint can vary widely. A Log10A pot should be 10% of the resistance at midpoint. But, again, this can be off 20%.
Let's take the case of a bass control which is typically wired as a rheostat. On one amp the pot might be 10% high and the midpoint 10% high. Therefore with the control at noon (assuming, say, a 1M pot) the resistance will be 121K. Another amp off the assembly line might be 10% low. Therefore the pot will be 81K. That's a 40K difference between the two amps and that's not even worst-case.
Now you can make the amps sound the same by simply turning down the control on one and/or turning it up on the other.
So when your friend says "well, no two amps sound the same" you can explain to him that they are probably more similar than not and a small twist of the tone controls will bring them into agreement.