In Russian internet slang, this phrase is an equivalent of ROFL - as if you laughed so hard that you fell under the table and go on laughing there.
Does Russian also have the idiom of "under the table" meaning illegal or off the books work ?
No. We say, for example, "Я работаю неофициально" (I work unofficially/off the books) or "У меня серая зарплата" (I have a "gray" salary, meaning that the employee gets his money in cash without paying taxes).
We have a similar idea in English. the "grey market" which is business that while not illegal is involved in extensive tax evasion.
Buying something on the grey market usually means purchasing the item from a dealer who has not been authorized by the manufacturer/distributor, and that often means that that item was intended to be sold in another country, and was imported into your country by your retailer without the permission of the manufacturer. While “grey market” items are often sold at discounted prices (as compared to items sold by authorized dealers), one does not always know that one is buying “grey market.” The danger of such a purchase is that the item may have different specifications than “authorized “ items; and, it is likely that there will be no warranty coverage in the event of a problem. In the words of the old Latin adage, Caveat emptor (Let the buyer beware).
Companies paying "gray" salaries, generally, are not considered "black market".
Because "black market" companies are selling illegally acquired goods, whilst companies paying "grey" salaries are simply practising tax evasion?
"Like the other cases, there are prepositions which can place whatever comes after them in the instrumental case. There are six in total: С(о), над, под, за, перед, and между."
From Russian/Grammar/Instrumental case - Wikibooks, open books for an open world