Should I be suspicious of meat/seafood on sale?

In the case of quickly perishable items like meat, when it's not an advertised sale, shops will sharply discount prices if they anticipate that they will be otherwise left with product beyond the sell-by date. So the answer to your question is both yes and no.

There is nothing wrong with buying something just before the sell-by date, but you do need to use or freeze it sooner rather than later. For everything but seafood, I jump all over those sales. I can barely tell the difference between super-fresh and right-at-the-sell-by-date for most items. Seafood is an exception for me, but that is just me. I will pay extra to get super-fresh seafood, even though I'll buy milk and meat right at the sell-by date if it saves me a few pennies.

So in this case, like many others, the key to making an informed choice lies in reading the label. No reputable grocery will alter the sell-by date. At least in the US, getting caught doing that will close a shop down and land people in jail. So read the label (or the tag on the meat-case window), and be informed about what you are buying.

A retailer at the markets that refuses a request for closer inspection by a prospective customer should be given a wide berth indeed. Rules of freshness apply to the retailer regardless of sale price. Use a little common sense when buying items on sale. Shopping at closing time is a great way to find bargains and makes your dollar go further. Check the premises of the retailer, are they clean and well maintained? What about the staff? Is the display cabinet in likewise condition? The tradition of garnishing trays of meat with sprigs of parsley is actually an important function. If the parsley is wilted and dead then that meat has most definitely been exposed to air for too long. If the display is messy and sloppy imagine what their cool room is like. That's the spot the customers don't even see.