Anyway, in the Blues tradition, parallel minor mode notes are used against major triads. That's how it is. For instance, a tune using A, D, E chords supports soloing using A minor pentatonic as well as A major pentatonic, as well as various ways of shifting between the two.

The superimposition of the minor pentatonic, major pentatonic and tritone (relative to the root) is known as the Blues scale.

There are situations in which the major-based intervals don't work that well against minor chords. A Blues tune using Am, Dm, E7 doesn't support A major pentatonic improvisation quite as well as *vice versa*: how well as A7, D7, E7 supports A minor pentatonic.

Now in this solo, firstly, everything is played half a step relative to the notation. Let's stick with how it's notated, though.

The solo is in E minor, and is using elements of harmonic minor, with the C, B7 dominant and the use of related notes in the solo.

Then in the next section, where the A-something chord in question occurs, the solo is not implicating any minor third against the A root at that point. It's not using the C#. Your tablature shows a bend down toward the 15th fret D. (What I'm hearing in the actual recording is that it's not actually a full bend; it's more than a semitone, but less than a full tone.
I slowed it down to 0.25 and repeated it a few times while playing the same thing, just to be sure.)

The D note which is the target of the bend, occurs in both the E natural minor (and the E minor pentatonic), and it occurs in E Dorian.

So in the case of that section of that solo, that is the simplest explanation why either an Am or A chord could work. They scales implicated by these choices both include the D.

For what it's worth, I seem to be hearing an Am chord. There are multiple rhythm tracks overlaid, and two strums are heard. The first strum is emphasizing the root and fifth, and then the second strum chimes in the higher notes. I seem to hear the second strum as minor,  particularly if I listen to just the right channel.