I believe I didn't expressly call out the Minimum Movement rule in the Leg Destruction section only because I wanted to try and cut down on page flips: why say "go to page X for the explanation" when I could just give it to you (same reason it tells you there that when prone that you can only change your facing by one hex, rather than "see the prone rules"). But in this case it seems to have caused a bit of confusion, and in any case, the TW wording I used is also a touch confusing on when the 1 MP status is applied and so could be clearer.
Replace the Leg Destruction entry on p. 44 with the following:
When a standing ’Mech loses a leg, the ’Mech automatically falls and ends its movement for that turn. The absent leg applies a +5 modifier to all Piloting Skill Rolls: this replaces all other PSR modifiers generated by damage to that leg.
A ’Mech with one leg is reduced to 1 Walking MP (this overrides all MP increases) and cannot run. Despite all this, it can still use the Minimum Movement rule (see p. 16), and so can make one attempt to stand (see p. 19) in each subsequent turn. In an exception to the normal rules, only one Piloting Skill Roll is required for this attempt, even if damage or other factors means that the attempt would normally require two or more PSRs (though all modifiers from any such factors still apply).
If the ’Mech manages to stand it can jump in subsequent turns, but a PSR is required each time it lands.
That should make it clear, hopefully without breaking anything else. My only concern is that I know I noted the odd wording on this while going over TW to write the BMM and yet kept much of it. Away from my notes, I can't recall if this was because there was some weird rule interaction that necessitated the wording, or if I was just being overly faithful to TW. As such, consider this tentative errata; if anyone spots an aspect I'm missing, let me know.
Note that the 1 MP is spent in the standing attempt, per p. 16: "It has at least 1 MP to spend"; "Such movement is the only MP it expends that turn". In other words, the 1 MP makes the standing attempt legal, but is also spent in the attempt, rather than making it possible but then hanging around to be spent afterwards. This also means that anything like heat that takes away that last MP means that you can't use Minimum Movement, and thus can't try to stand. I'll also touch up p. 16 a little bit to clarify this.