The issue here is that you're looking mostly at Pliny :) Pliny is a wonderful glimpse into the Roman world, and he did some excellent work in ecology and such, but he also likes reporting rumours, such as that sub-Saharan Africans had eyes and mouths in their belly and things like that. He was by no means a medical mastermind. The work you're looking for - and, incidentally, the most complete work purely on medicine in that time period - is Celsus' On Medicine. While yes, he does note some "folk remedies" that you mentioned, he also does note that they were...well...folk remedies.

For example, one of the ones I remember offhand most clearly is in his section on angina (random chest pains, they can be a sign of something worse). I quote:

I hear it commonly said that if a man eat a nestling swallow, for a whole year he is not in danger from angina; and that when the disease attacks anyone it is also beneficial to burn a nestling which has been preserved in salt and to crumble the powdered ash into hydromel which is administered as a draught. Since this remedy has considerable popular authority, and cannot possibly be a danger, although I have not read of it in medical authorities, yet I thought that it should be inserted here in my work.

Basically tl;dr'd into a "I've heard people say this, and while I can't prove it's true, it can't hurt. Go for it." (Nota bene - don't do this. If you have angina, go see a doctor.)

One essential thing to remember is that there was no "central school" for medicine. Doctors learned from other doctors (apprenticeship), and therefore kooky traditions would be passed on religiously down the line. By far the best doctors generally were those who were attached to the legions, because, even when those legions were garrisoned, there was a constant stream of injuries which had to be treated. The Romans were pretty incredible at battlefield medicine, able to do everything from trepanning to fix a cracked skull/hematoma to fixing basically any flesh wound ever. Book 7, for example, is on surgeries, while Book 5 does a quite a bit of discussing on flesh wounds. His discussion of how to stitch things really is pretty good:

The suture or fibula should take up, not only skin but also some of the underlying flesh, where there is any, that it may hold more firmly, and not tear through the skin. And both are best used with a strand of a soft wool not too closely twisted that it may cause less irritation to the body, and both should be inserted at intervals not too distant or too close. For if the intervals are too distant, the wound is not held together; if too close, it is very hurtful, for the more often the needle this fixes the tissues, and the more places are wounded by the inserted stitches, the worse is the inflammation set up, especially in summer. Neither procedure needs any force, but is useful just so far as the skin follows that which draws it as if of its own accord. Generally, however, fibulae leave the wound wider open, a suture joins the margins together, but these should not be brought actually into contact throughout the whole length of the wound, in order that there may be an outlet for any humour collecting within. If any wound admits of neither of these, it should none the less be cleaned. Hence, upon every wound there is to be applied, first a sponge squeezed out of vinegar; or out of wine if the patient cannot bear the strength of vinegar. A slight wound is even benefited if a sponge is applied wrung out of cold water. But in whatever way it is put on, it is only of service while moist; and so it must not be allowed to become dry.

Regarding germ theory! Yeah, that wasn't a thing. It's kinda hard to realize that there are invisible (to the human eye) microbes everywhere that cause infections and such - hell, it took us centuries after the Byzantines fell to formulate that theory. Medicine for the Romans (and, incidentally, for everyone after them until germ theory) was all about correcting the bodily "humours" - ensuring that each of the elements was in balance with the others. If you had too much blood, for example, some needed to be drained. That kinda thing. For example, he notes on seasonal allergies in this way:

In spring those diseases are usually to be apprehended which are stirred up anew by movement of humor. Consequently there tend to arise runnings from the eyes, pustules, haemorrhages, congestions in the body, which the Greeks call apostemata, black bile which they call μελανχολία, madness, fits, angina, choked nostrils, runnings from the nose. Also those diseases which affect joints and sinews, being at one time troublesome, at another quiescent, then especially both begin and recur.

They did, however, recognize the power of antibiotics, even though they had no idea why they worked so well. For example, in the book on surgery that I just linked a couple of paragraphs up...

Therefore whenever it is dressed, the abscess cavity should be washed out, with wine mixed with rain water or with a decoction of lentils, when the discharge seems to need checking; with honey wine when cleaning is required; after which it is dressed as before. When the discharge appears to be checked, and the cavity clean, then is the time to help the growth of flesh, both by irrigating with equal parts of wine and honey, and by laying on a sponge soaked in wine and rose oil.

Alcohol (usually rubbing alcohol) and honey are both still pretty widely known as fantastic antiseptics, as well as clean water (rainwater) for general cleaning. Additionally, Celsus does note that it's a bad idea to "take a bath" while ill or soon after surgeries. This sounds like terrible advice until you remember that baths were communal, and it was WAY more likely for something to get infected if you were taking communal baths together (especially because there was no chlorine to keep the water relatively clean).

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There is a good bit of stuff that's just a bad idea to try in Celsus' compendium - medicine was trial and error, and if one person got better while taking a particular remedy, it could be noted as a potential cure. Even so, Roman doctors did take quite a few remedies from Greek doctors (as noted within Celsus) - Hellenophilia was a pretty big thing :)

Hope that answered your question!