There are a few things with Marey's assertion that 'all their products meet the hight standards of UL.' Now is a good time to go into them.

First of all, UL does not have "high standards;" nor has UL anything to do with quality control. UL is in the sole business of, as their motto states, 'testing for public safety.' Not a single standard of theirs has the slightest thing to do with quality. We've all seen some pretty poorly made items that met every UL requirement.

Next, who says they meet any standards at all? MAREY does. Marey can claim what they want; absent the UL label on the product, there is NO UL listing for that product.
Indeed, many companies only apply the UL label to a part of their production. The UL listing applies only to those items that actually have the UL label. It matters not whether the unlabeled products are the same - or not.
I'm not surprised, either, that UL has never heard of "Marey." I seriously doubt that Marey actually makes anything; they are a marketing outfit. The UL tag will identify who actually made the item - either by name, or with a file number (used internally by UL).

Finally, every UL standard references other codes and standards. UL is not about to list a product that either directly violates those other codes, or whose instructions tell you to do so. Were such a product as this heater to be submitted to UL for evaluation, I expect that UL would have serious objections about the following points:
1) No GFCI in the plug;
2) The plug not being appropriate for the electrical requirements of the device;
3) The length and size of the cord;
4) The sealing of the connection box; and,
5) The instructions for use.

Apart from the NEC, other codes UL would reference would include the ASME's "Boiler and Pressure Vessel" code, and the requirements of the National Safety Foundation.