Is it bad to let air into my primary fermenter?

Any way you take a sample (unless it's from a pressurized vessel with an outlet) will draw air in. As you suspect, it should be a small amount, and given that your beer A) may still be fermenting (which CO₂ will help strip any introduced oxygen out of the beer) and B) definitely still has yeast in it (which will scavenge oxygen, as long as it's still alive), it should be just fine. If you prime and bottle-condition as well, the re-fermentation will give an added layer of protection from oxygen.

However, it's always best practice to avoid contact of any kind with air, as even small amounts of oxygen can be damaging to the beer's flavor. The 'CO₂ blanket' often referred to is not a viable solution for keeping beer exposed to air (even just by small gaps around the lid/bung) safe from oxidation. While CO₂ is indeed heavier than air, it, along with oxygen (and all other gasses), will always diffuse to take up the whole volume available for it, eventually making a homogenous mixture of the gasses present. Gasses also travel from areas of higher concentration to lower concentration (meaning CO₂ will tend to diffuse out the gaps and air will tend to diffuse in). In other words, any air that gets in will not simply sit atop the CO₂, but will rather mix with it until the whole head-space volume is an even mixture of CO₂ and any introduced air (letting air touch the beer/head-space boundary and hence enter the beer), and this will continue until the gasses on either side of the leak are in equilibrium (these behaviors are described by the ideal gas law). Luckily, this takes a while and may be of little consequence to the quality of your beer if you don't leave it too long.

Since CO2 is heavier than oxygen, it won't escape the container unless you have a wind blowing over the opening. Also, the beer will be generating more CO2 as i ferments, so even if any escapes, more will replace it. I don't think it would be a problem to leave a small hole.