I agree with all of you. I was recently critiqued on this point during an annual observation for flying exactly 250, and in a multi-decade flying career had never been questioned on it before. I was just wondering if I had somehow missed out on a bit of airmanship or if my observer was just being overly critical.
Yes, many countries are strict about 250 below 10,000, especially Germany in my experience. They will often deny high speed climb even to a 747 or MD11, both of which often need to be 270+ to climb clean, necessitating that you leave flaps down until reaching 10,000 on climb out at heavy weights.
However, in the USA I would cite this section of the Aeronautical Information Manual (not regulatory, but advisory in nature):
4−4−12. Speed Adjustments
a. ATC will issue speed adjustments to pilots of
radar−controlled aircraft to achieve or maintain
required or desire spacing.
b. ATC will express all speed adjustments in
terms of knots based on indicated airspeed (IAS) in
5 or 10 knot increments except that at or above FL
240 speeds may be expressed in terms of Mach
numbers in 0.01 increments. The use of Mach
AIM 10/12/17
4−4−8 ATC Clearances and Aircraft Separation
numbers is restricted to turbojet aircraft with Mach
meters.
c. Pilots complying with speed adjustments are
expected to maintain a speed within plus or minus
10 knots or 0.02 Mach number of the specified speed.
d. When ATC assigns speed adjustments, it will
be in accordance with the following recommended
minimums:
1. To aircraft operating between FL 280 and
10,000 feet, a speed not less than 250 knots or the
equivalent Mach number.
NOTE−
1. On a standard day the Mach numbers equivalent to
250 knots CAS (subject to minor variations) are:
FL 240−0.6
FL 250−0.61
FL 260−0.62
FL 270−0.64
FL 280−0.65
FL 290−0.66.
2. When an operational advantage will be realized, speeds
lower than the recommended minima may be applied.
2. To arriving turbojet aircraft operating below
10,000 feet:
(a) A speed not less than 210 knots, except;
(b) Within 20 flying miles of the airport of
intended landing, a speed not less than 170 knots.
3. To arriving reciprocating engine or turboprop
aircraft within 20 flying miles of the runway
threshold of the airport of intended landing, a speed
not less than 150 knots.
4. To departing aircraft:
(a) Turbojet aircraft, a speed not less than
230 knots.
(b) Reciprocating engine aircraft, a speed not
less than 150 knots.
e. When ATC combines a speed adjustment with
a descent clearance, the sequence of delivery, with the
word “then” between, indicates the expected order of
execution.
EXAMPLE−
1. Descend and maintain (altitude); then, reduce speed to
(speed).
2. Reduce speed to (speed); then, descend and maintain
(altitude).
NOTE−
The maximum speeds below 10,000 feet as established in
14 CFR Section 91.117 still apply. If there is any doubt
concerning the manner in which such a clearance is to be
executed, request clarification from ATC.