There certainly could be reasons why a turntable mat could alter bass performance.
The first and most likely is better isolation of the disc from LF vibration interference from the speakers. This is a well known and common problem with LP reproduction and certainly does have its maximum deleterious effects in the bass decade. That is why I isolate my turntable inside cabinets and take constructional steps to minimize this. In the hey day, turntables were nearly always enclosed in substantial cabinets. This lasted until the introduction of the ubiquitous plinth from the Far East. When I bought three of the four turntables I own they never came with a plinth. As I have said before in those days, you bought a turntable, pickup arm and cartridge. You were supposed to have enough "chops" to sort this out and make a good job of it. If not you were condemned to a ghastly table player or radiogram with a dreadful auto changer.
The other reason might be that some turntables may have some excess rumble, and the mat provides an extra measure of isolation. This would improve bass also.
Turntable reproduction is very fickle. Small problems of set up and installation have a disproportionate effect to downgrade results.
Many turntables do not even allow for proper set up. When it comes to PU arms there are far more bad ones than good ones. SME really have been at the head of the pack. Their introduction of the silicon fluid damper, was a game changer in my view.
Next obsessional record care and handling is essential. In my collection pops and ticks are rare, and it does sound like a CD.
I think a lot of the vinyl is better than CD comes from two issues.
In the hey day of the LP companies had career engineers who worked with usually one company for a life time and really know their craft. So the recordings were better then now in a great many cases.
In addition there are analog to CD transfers that are less then stellar, with the LP being better then the CD. There are a few of those I have come across.
I think the biggest reason though is that the dynamic range of an LP is by necessity restricted. This on the one hand limits the amount of dynamic compression that can be applied to pop music.
On the other hand I think there are still many systems that do not actually cope with the wide dynamic range of digital music. This is particularly true of speakers. A great many lack sufficient power band response in critical areas, and add their own dynamic compression along with distortion. It really does take an incredible speaker system to really cope with the dynamic that good digital sources have to offer. Then we also get into clipping in the amplification part of the equation. This is not only in the power amp end of things, but I have found many units over the years designed with insufficient headroom in the preamp stages. I have a feeling this is still likely prevalent. These issues can give a definite advantage to LP over digital sources in many systems.
