You're still setting up a false dichotomy.
Responsibility confers both ability and accountability.
So I decided to look into the numbers around the defending-Washington thing.
Strength required to defend Washington: 40,000 (per corps commanders), as:
15,000 in the forts, or enough to man them
25,000 covering force in Virginia (Manassas to Harpers Ferry)
27 March: Stanton determines that troops in the Shenandoah Valley do count as able to defend Washington.
By 4th April - Stanton argues that troops in the Shenandoah Valley do NOT count as able to defend Washington.
McClellan's plan was:
Baltimore - 7,388 after railroad guards
Washington - 10,600 manning the fortifications
11,400 disposable troops (i.e. a force surplus to the defences) of whom 4,000 ordered to Manassas (total 22,000)
4,000 new troops in NY ordered to Washington
3,500 new troops in Pa ordered to Manassas
Guarding the railroads in Md: 3,359, to be relieved and sent to Manassas
Abercrombie's force at Manassas including Geary and some cavalry: 7,780 (with 12 field guns)
In the Shenandoah was Banks' 5th Corps and Blenker's division of 2nd Corps: 29,715 (with 24 field guns)
And 3,652 cavalry and the railroad guards (2,100)
And "some regiment" plus 500 cavalry to be 1,350 men total on the lower Potomac.
Which McClellan presented as being desired as:
7,780 at Warrenton
10,859 at Manassas
35,467 in the Shenandoah Valley
and 1,350 on the lower Potomac
For 55,456 total
Plus 18,000 for "the garrisons and the front of Washington".
Or 73,456 (for which the 4,000 NY troops were extra and should go to Washington). Interestingly Baltimore is mentioned but the strength is not actually used anywhere in his listing.
The combined strength of Banks, Blenker and Abercrombie is 37,495, though his number for Abercrombie includes an unspecified amount of cavalry and Geary's Independent Brigade.
Actual strengths at these points, all Present, from 31 March report unless otherwise noted:
Washington district: 20,795 (McClellan overcount by 1,205)
5th Corps (exc. Blenker) 23,607.
Blenker as 1/3 of 2nd Corps: 9,302 (combined strength 32,909, McClellan overcount by about 4,500 minus however large Geary's Independent Brigade was)
Alexandria district: 1,404 (presumably included in the Washington count by McClellan? This negates that overcount entirely and turns it into an undercount by 199)
Railroad Brigade 4,993 (April, McClellan undercount by 1,600)
Baltimore 6,717 (30th May, McClellan overcount by 600 but not part of his direct scheme - probably the movement of regiments between 1 April and 30 May)
No known strengths for:
Shenandoah railroad guards, cavalry
Lower Potomac force
Total 60,101 as:
22,199 in or around Washington directly
Railroad Brigade and Banks as covering force: 37,902, plus Geary
plus 6,717 in Baltimore.
Add the troops en route and you're up to 74,318, plus Geary, or 67,601 + Geary without the Baltimore force.
So the amount of troops McClellan left defending Washington comes in the lowest possible calculation to 55,108. This calculation discounts some line-of-communication troops McClellan included and several new regiments which McClellan already had under orders (and included), and his ops plan included leaving a whole extra corps in the Manassas area until the situation around Washington was safe.
The document he wrote was outlining the situation as it would be when he had taken his whole army to the Peninsula, which had not yet taken place; it's not surprising that it included some troops who were still en route. What it looks like is that McClellan's numbers are probably correct apart from double counting a brigade somewhere and assuming the arrival of some new regiments which had not yet arrived, and perhaps being a little overzealous in identifying LoC troops to relieve by new troops and send to the front.
Either way, however, he has definitely exceeded the 40,000 considered to be the minimum required by the corps commanders - and not by a small amount, either.
The argument used against McClellan was actually that the defences of Washington were insufficiently garrisoned because Wadsworth didn't have enough men Present to do the tasks required, this number being reached by taking the 20,795 and discounting the troops sick or under arrest. This was presented as the entire defence of Washington and used to raise the alarm by Stanton, though in fact less than a week prior Stanton had concurred that troops in the Shenandoah did indeed count as available to defend Washington.
The ultimate fate of 1st Corps after it was witheld, furthermore, was not to be used in the Washington defences to show the men in the capital that they were being defended or to bolster the apparently flawed strength of those defences. Instead they were used to hold the line of the Rappahanock and swelled the covering force to an absurd degree - as of mid April it comprised six divisions, while McClellan's main force composed eight. (Total Present defending Washington at this point exclusive of Baltimore or line of communcation troops 91,000; total Present in McClellan's army at this point about 95,000.)
Of course, it's always going to be a bit absurd to simultaneously hold these views:
1) We need 35,000 more troops to defend the capital, let's take them from our main effort against the enemy.
2) I think our main effort against the enemy will win the war in a few weeks, let's not bother recruiting any more troops.