The popular question "What is the relationship between SWR and receive performance?" asks if a receiver with a well-matched antenna (low SWR) beats a receiver with a poorly-matched antenna, with everything else being equal. The consensus opinion of the answers, weighted according to the votes on the answers, is no; the two receivers should receive about the same.
The idea is that an impedance mismatch leads to power loss, and a weaker signal at the receiver. But losses shouldn't affect receiver performance as long as the signal-to-noise ratio (SNR) is the same, because the receiver's automatic gain control (AGC) feedback circuit can easily add a few more decibels of gain to compensate for any such losses. There is an important caveat to this rule that the received RF noise floor must be above the receiver's noise floor, because otherwise the signal-to-noise ratio will be affected.
This logic makes sense to me, and I can find no flaws in it. But if that is so, then why is it that when I use my manual T-network transmatch (antenna tuner) to tune my ZS6BKW antenna on various HF bands such as 40m and 20m, I can get a fairly good match without transmitting by turning the knobs to maximize the band noise in my headphones? (I say "band noise" because I tune the radio to an unused frequency and then adjust the transmatch for maximum static, but if there were a signal on the frequency then I would adjust the transmatch to make the signal the loudest.) If the consensus answers to the other question are correct, then I would think that turning the knobs would make no difference at all to the volume of sound in the headphones.
My HF rig is an Elecraft K2, which has an excellent receiver. The caveat to the rule shouldn't apply, because the RF noise floor should be well above the receiver's noise floor on 40m and 20m.