Yes and no actually. Unless the fresh veggies or fruit come from someone's home garden or a farmer's market, I have to disagree. Absolutely, fresh fruit and veggies grown the old-school way are best. But if it's a choice between the "fresh" produce in a supermarket or the best canned/frozen it's the latter every time. The "fresh" stuff will likely have been waiting to be purchased for weeks, whereas the best canned/frozen food is minimally processed, picked at the height of ripeness, and stored instantly. Ironically, this means that I can often find a fresher taste from a can or frozen package.
With that said though this also means reading labels to find the best canned/frozen products. For example Muir Hill make the best canned tomatoes, but you want to avoid the heck out of Monsanto's or anyone else who puts corn syrup or other unnecessary stuff in there. Yuck! You also want to avoid anything that's been cooked too much before being canned or frozen.
When it comes to buying spinach in particular frozen can actually be wiser if you're short on money because spinach is so watery. You get a LOT more spinach for your money that way. But if your financial state is such that you don't have to worry about that, then the fresh is what you'll probably prefer.